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modem science

and its philosophy

PHILtPP FRANK

modern science
and its philosophy

HARVARD UNIVERSITY PRESS • CAMBRIDGE • 1949

LONDON -GEOFFREY CUMBERIEGE • OXFORD UNIVERSITY PRESS

BY THE PRESIDENT AND PELIOWS OF HARVARD COLLEl
PRINTED IN THE UNITED STATES OF AMERICA

DEDICATED TO

MANIA

IN REMEMBRANCE. OF THE FAST
AND ANTICIPATION
OF THE FUTURE

PREFACE

Along with the evolution of twentieth-century science, philosophi-
cal ideas were developed which have sprouted and grown on the soil
of this science. In this book I present my thoughts on this develop-
ment, in the sequence in which they entered my mind during the
many years of my teaching and research work in science. If we want
to evaluate precisely and critically how firmly this philosophy is an-
chored in the ground of science, we must not ignore the extrascientific
factors, but must analyze carefully the social, ethical and religious in-
fluences. Every satisfactory philosophy of science has to combine logic
of science with sociology of science.

Since 1940 not only have I been teaching science, but Harvard
University offered me the opportunity of teaching also the philosophy
which, in my opinion, has grown up along with twentieth-century
science. A large part of this book reflects the experience that I have
% gained by observing the interests of the students and their reactions
to my teaching.

My work has been stimulated greatly by the Harvard experiment
in General Education, in which I have had the privilege of participat-
ing. The Harvard University Press has been of substantial help to me
in finishing this book. I am particularly obliged to Miss Eleanor R.
Dobson and Mr. J. D. Elder for their fine spirit of cooperation. I hope
that the Harvard Press will soon publish a volume which is written
along similar lines, the lucid and straightforward book ‘‘Positivism,”
by R. von Mises.

PmLTPP Frame

CONTENTS

^ introduction . historical background - J

<1. experience and the law of causality 53

j2.' the importance for our times of Ernst Mach's philosophy of

science 61

3. Ernst Mach and the unity of science 79

4. physical theories of the twentieth century and school philosophy 90

5. is there a trend today toward idealism in physics? 122

6. mechanical "explanation" or mathematical description? 138

7. modern physics and common sense 144

8. philosophic misinterpretations of the quantum .theory 158

9. determinism and indeterminism in modern physics 172

10. how idealists and materialists view modern physics 186

11. logical empiricism and the philosophy of the Soviet Union 198

12. why do scientists and philosophers so often disagree about the

merits of a new theory? 207

•13. the philosophic meaning of the Copernican revolution 216

14. the place of the philosophy of science in the curriculum of the

physics student 228

science teaching and the humanities 260

/1 6. the place of logic and metaphysics in the advancement of modern

science 286

bibliographical note 305

index 307

INTRODUCTION

HISTORICAL BACKGROUND

1. Discusilons in a Vienna CofFee House

At the time when the first chapter of this book was written (190f )
I had just graduated from the University of Vienna as a doctor of phi-
losophy in physics. But the domain of my most intensive interest was
the philosophy of science. 1 used to associate with a group of students
who assembled every Thursday night in one of the old Viennese coffee
houses. We stayed until midnight and even later, discussing prob-
lems of science and philosophy. Our interest was spread widely over
many fields, but we returned again and again to our central prob-
lem: How can we avoid the traditional ambiguity and obscurity of
philosophy? How can we bring about the closest possible rapproche-
ment between philosophy and science? By “science” we did not mean
“natural science” only, but we included always social studies and the
humanities. The most active and regular members of our group were,
besides myself, the mathematician, Hans Hahn, and the economist,
Otto Neurath.

Although all three of us were at that time actively engaged in re-
search in our special fields, we made great efforts to absorb as much
information, methodology and background from other fields as we
were able to get. Our field of interest included also a great variety of
political, historical, and religious problems which we discussed as
scientifically as possible. Our group had at that time no particular
common predilection for a certain political or religious creed. We had,
however, an inclination towards empiricism on one hand and long
and clear-cut chains of logical conclusions on the other. There were
quite a few occasions on which these two predilections did not mix
very well.

This apparent internal discrepancy provided us, however, with a cer-
tain breadA of approach by which we were able to have helpful discus-

modern science and its philosophy

sions with followers of various philosophical opinions. Among the par- ‘
ticipants in our discussions were, for instance, several advocates of
Catholic philosophy. Some of them were Thomists, some were rather
adherents of a romantic mysticism. Discussions about the Old and New
Testaments, the Jewish Talmud, St. Augustine, and the medieval
schoolmen were frequent in our group. Otto Neurath even enrolled for
one year in the Divinity School of the University in order to get an ade-
quate picture of Catholic philosophy, and won an award for the best
paper on moral theology. This shows the high degree of our interest
in the cultural background of philosophic theories and our belief in
the necessity of an open mind which would enable us to discuss our
problems with people of divergent opinions.

At that time a prominent French historian and philosopher of sci-
ence, Abel Rey, published a book which later was to make a great im-
pression upon me. At the turn of the century the decline of mechanistic
physics was accompanied by a belief that the scientific method itseli^
had failed to give us the “truth about the universe”; hence nonscientific
and even antiscientific tendencies gained momentum. I quote some
passages in which Rey describes this situation excellently and pre-
cisely.

Fifty years ago, he says, the explanation of nature was believed to
be purely mechanical.

It was postulated that physics was nothing but a complication of me-
chanics, a molecular mechanics . . . Today [1907] it seems that the picture
offered by the physical sciences has changed completely. The general unity
is replaced by an extreme diversity, not only in the details, but in the leading
and fundamental ideas . . . [This accounts for] what is called the crisis
of contemporary physics. Traditional physics assumed until the middle of
the nineteenth centiny that it had only to continue its own path to become
the metaphysics of matter. It ascribed to its theories an ontologic value, and
these theories were all mechanistic. Traditional mechanistic physics was
supposed, above and beyond the results of experience, to be the red, cog-
nition of the material universe. This conception was not a hypothetical
description of our experience; it was a dogma.

The criticism of the traditional mechanistic physics that was formu-
lated in the second half of the nineteenth century weakened this assertion
of the ontologic reality of mechanistic physics. Upon this criticism a philos-

historical background

*ophy of^hysics was established that became almost traditional toward the
end of the nineteenth century. Science became nothing but a symbolic pat-
tern, a frame of reference. Moreover, since this frame of reference varied
according to the school of thought, it was soon discovered that actually noth-
ing was referred that had not previously been fashioned in such a way that
it could be so referred. Science became a work of art to the lover of pure
science, a product of artisanship to the utilitarian. This attitude could quite
rightly be interpreted as denying the possibility that science can exist. A
science that has become simply a useful technique ... no longer has the
right to call itself science without distorting the meaning of the word. To
say that science cannot be anything but this means to negate science in the
proper sense of the word.

The failure of the traditional mechanistic science . . . entails the prop-
osition: “Science itself has failed.” . . . We can have a collection of em-
pirical recipes, we can even systematize them for the convenience of
memorizing them, but we have no cognition of the phenomena to which this
system or these recipes are applied.*

Our group was formed during the period which was so eloquently
described by Rey. His book was discussed frequently by us in the last
years of my stay in Vienna (1908-1912). The problems raised and the
results obtained are reflected partly in Chapter 2 of this book. The
general reaction of our group to the intellectual and cultural situation
depicted by Rey can be described as follows:

We recognized the gradual decline in the belief that mechanistic sci-
ence would eventually embrace all our observations. This belief had
been closely connected with the belief in progress in science and in
the scientific conception of the world. Therefore, this decline brought
about a noticeable uneasiness. Many people lost their faith in scientific
method and looked for some other method which might yield a real
understanding of the world. A great many people believed, or at least
wanted to believe, that the time had come to return to the medieval
ideas that may be characterized as the organismic conception of the
world.

In the history of science and philosophy there have always been di-
vergent opinions about the conditions under which we may say that a

*A. Rey, La ThSorie de physique chez les physiclens contemporains (Paris,
1907), pp. 16 £F.

modern science and its philosophy

scientific theory has “explained” a certain range of observations. Some^
authors have maintained that only an explanation by mechanical causes
and by the motion of material particles can satisfy our intellectual curi-
osity. Others have claimed that the reduction to mechanical causes is
only a superficial explanation and not a real one. Some of the opponents
of the mechanistic world view have stated that all phenomena must
b,e interpreted in terms of the evolution of an “organic whole” in order
really to understand them. The decline of the belief in mechanistic sci-
ence seemed to favor this organismic view, which has been attractive
to many because of its religious and social implications. In this way
there had arisen at the turn of the century what some called a crisis in
science or, more accurately, in the scientific conception of the world.
For more than two centuries the idea of progress in science and human
life had been connected with the advance of the mechanistic explana-
tion of natural phenomena. Now science itself seemed to abandon this
mechanistic conception, and the paradoxical situation arose that one
could fight the scientific conception of the world in the name of the
advance of science.

2« The Failure of Mechanistic Science

The sixteen chapters of this book have been written over a period of
almost forty years. They are all meant to be contributions to one task:
to break through the wall which has separated science and pliilosophy
for about one and one-half centuries. The book reflects the methods by
which this wall has been besieged in the twentieth century. During the
last decades of the nineteenth century, a revolution in physical science
started which has itself brought about a revolution in our general scien-
tific thought. The methods that have been tried in the fight for the unity
between science and philosophy have changed along with the advance
of science.^ wo characteristic beliefs of nineteenth-century science
broke down during its last decades; these were the belief that all phe-
nomena in nature can be reduced to th e laws of mechani cs, and the
belief that science will eventually reveal the “truth” about the univers^
In the twentieth century the revolutionary changes in science de-
veloped with ever-increasing rapidity and intensity. It is no wonder

historical background

*that thijf rapid transformation of scientific thought has been accom-
panied by rapidly changing methods in the scientist’s approach to phi-
losophy and in the philosopher’s views on science.

The chapters of this book have played their part in this developing
and changing fight for the unity of science and philosophy. Through
them we can pursue a pattern that has grown from rather tentative
and naively empirical beginnings to a more and more abstract tech-
nique. In order to understand this evolution precisely, it is not su:^-
cient to follow the gradual alterations from the purely logical angle.
We must also consider carefully the historical trend and background
of the arguments.

Rey had the strong feeling that the place of physics in human
thought had dangerously deteriorated. He says:

The physicochemical sciences are an effort made by man to explain
sensed nature or what is perceived by our senses . . . The importance of
this effort has been understood in all periods of history. So early a thinker
as Epicurus believed that physics was the basis of the effort to liberate
the human mind from its blind instinct to believe, from its prejudices and
its superstitions . . . Everyone would agree that^modem positivism has
been nothing but an attempt to extend to all the departments of human
knowledge, without exception, the general method and conception of sci-
ence, that is, science constructed according to the example of physicsj)the
spirit of positivism and the spirit of science have become synonymous in
current speech.

If these sciences, which historically have played essentially an emancipa-
tory role, were tarnished by a crisis that leaves them no other value than that
of recipes which are technically useful and that deprives them of any sig-
nificance in the cognition of nature, a complete upset in the art of logic and
in the history of ideas must result.(^hysics loses all its educational value;
the positive spirit which it represent is a misleading and dangerous spirit.
Reason, rational method, and experimental method must be considered in
good faith as having no cognitive value. All these methods are, then, pro-
cedures of action, not means of cognition. They can be developed in order
to obtain certain practical results, but we must be well aware that they have
no value except in their restricted domain. The cognition of the real must
be sought or be given by other means. We must guard against the danger-
ous illusion of rationalism and scientism. It is important to know that by this
method the real is ignored and that physics leads to ignorance and not to
cognition of real nature . . ])

modern science and Its philosophy

If the problem of the cognition of nature and of the posslbili^ of ther
physicochemical sciences remains in the same form in which it has devel-
oped from the Renaissance to the time of positivism, the rational and posi-
tive method remains the supreme educator of the human mind, in the
domain that is accessible to it, of course, T o give the mind a scientific atti-
tude in the sense that has been understood by positivism and positive
physics remains the necessary and sufficient condition of intellectual sanity.
Physics is the school where one learns to know things.^

(

3. Ernst Mach's Purge of Traditional Physics

,jjn this critical situation our minds turned towards a solution that
had been advanced about twenty-five years before by our local
physicist and philosopher, Ernst Mach. He maintained that “explana-
tion" by reduction to a system of cherished conceptions is pure illu-
sion. If all the multitude of observable phenomena are reduced to
mechanical or organismic phenomena, these special types of phe-
nomena chosen as the basis of explanation are by themselves no more
understandable than the phenomena that are to be explained. Maeh
claimed that there is no essential difference be tween a n “e xplanation"

1 and a "desc ription." In our everyday language the word “description”

I refers to a single ev ent or phenomenon. We^ “describe” the fall of a
specific stone at a specific time and place. If, however, we formulate
Galileo’s law of freely falling bodies, which tells us that all bodies fall
with an equal constant acceleration, we describe the fall of a great
-many bodies under different circumstances. This description of a_
class of phenomena is called by Mach a “physical law” or an “explana-
tion.” If an explanation is nothing but a^ descripti on of many cases
1 by a short sentence, it cannot matter much whether the "explanation”
is given by feduCfioh to the laws of mechanics or to the laws of electro-
I magnetism or even of statistics.^

' In this way Mach separated the conception of “scientific explana-
tion” from “mechanical explanation.” He saved the scientific world pic-
ture from going down along with the mechanistic picture. Similar ideas
had been advanced by other writers in Mach’s time, but none formu-
lated them with so much lucidity and breadth of approach. No one else

* Ibid., pp. 18 ff.

historical background

* ancho];^ d tliem so firmly in the soil of science, in physics as well as in
biology and psychology.

Although Mach’s views were the principal background of our
thoughts, they were not the most powerful stimulus to our actual
work. Our group fully approved Mach’s antimetaphysical tendencies,
and we joined gladly in his radical empiricism as a starting point;
(but we felt very strongly about the primary role of mathematics and
logic in the structure of science. It seemed to us that Mach had not
done full justice to this aspect of science. We felt that considering the
principles of science as nothing but abbreviated descriptions of sense
observations did not account fully for the fact that the principles of
science contain simple clear-cut mathematical relations among a small
ni’.mber of concepts, whereas every description of observations con-
tains a great number of vague connections among a great number of
vague concepts. We also felt that to call the principles of science “eco-
nomic descriptions of observations” was not to do justice to the pre-
dominant role of reasoning in the discovery and presentation of these
principles^ We were even attracted by some tenets of Kant’s theory of
knowledge, particularly by his “Introduction to Any Future Meta-
physics that may Present Itself as Science.” ^e saw much truth in
Kant’s statement that the recording of observations is not a purely
passive act but that a great deal of mental activity is necessary in order
to formulate general statements about sense observations.) '

The human mind, according to KanL-can desc ribe n atural phenom-
ena only by using a certain j)a ttero, c ertain forms of thinking that a re
produced by the observing mmd an3~are~not prwided by the ob-
served physical object. Since these “forms" or “patterns of experience”
are provided by the human mind and not by the physical facts, they
cannot be changed by the advance of scientific investigations^The ma-
terial delivered by sense observation can be manufactured into a scien-
tific system only by adding forms of experience that are determined by
the nature of the human mind^ur whole group understood and fully
agreed that the human mind is ^rtly responsible for the content of sci-
entific propositions and theories. But we also felt strongly that an
orthodox belief in Kant would lead us into a new type of metaphysics.

modern science and its philosophy

not less unscientific than medieval metaphysics. For instancy, Kant, '
and even more, many of his followers, maintained that the axioms of
Euclidean geometry or Newton’s laws of motion are forms of experi-
ence that are produced by the organization of the human mind. This
would imply that no advance in these fundamentals of science will be
possible without changing the nature of human mind. However, about
1900, scientists became accustomed to envisaging the possibility of!
changes in the principles that had been traditionally regarded as self-
evident axioms^ Non-Euclidean geometry was no longer considered
a purely logical exercise, but was recognized as a serious system of
geometry. This new conception, along with Mach’s criticism of New-
ton’s mechanics and with the new electromagnetic theory of matter,
opened a path for some(^doubts whether Newton’s laws of motion were
actually the final 'word about the nature of the universe. A step in the
same direction was the statistical interpretation of thermodynamics,
which suggested the superposition of statistical laws on dynamical
laws. As enthusiastic students of contemporary science our group re-
jected Kant’s doctrine that the forms of experience provided by the
human mind were unchangeable. We looked for some way to construe
these forms as subject to an evolution that would be in accord with the
evolution of science. We felt very strongly that there was a certain gap
between the description of observations, necessarily vague and com-
plex, and the principles of science, consisting, in physics particularly,
of a small number of concepts (like force, mass, etc.) linked by state-
ments of great simplicity.^We admitted that the gap between the
description of facts and the general principles of science was not fully
bridged by Mach, but we could not agree with Kant, who built this
bridge by forms or patterns of experience that could not change with
the advance of scienc^

4. Henri Poincare and a ''New Positiviim"

In our opinion, the man who bridged the gap successfully was the
French mathematician and philosopher Henri Poincar6. For us, he
was a kind of Kant freed of the remnants of medieval scholasticism
and anointed with the oil of modem science.

historical background

^ Kaat had claimed that there would never be another way to organ-
ize our experience than by Euclidean geomet ry and Newtonian me-
chanics. But at the turn of the century non-Euclidean geometry had
been established, although its importance for physical science was not
completely understood. Departures from Newtonian mechanics were
already in the making. We understood that Kant’s erroneous conception
of geometry and mechanics must have its source in his erroneous ajti-
tude toward the relation between scifincft and philosophy . )

At this time I was very much interested in the criticism launched
by Nietzsche against Kant’s idealistic philosophy. Kant’s primary aim j
was to answer the question of how the human mind can make state- 1
ments about facts of the external world with absolute certainty even if
these assertions are not the result of experience about this world. For
Kant, the propositions of Euclidean geometry were a convincing ex-
ample of assertions of this kind. By claiming that the axioms of geom-
etry are forms of experience produced by the human mind, Kant ex-
plained man’s ability to produce these assertions without external ex-
perience. Nietzsche said flippantly that Kant’s explanation is merely
equivalent to saying that man can do it “by virtue of a virtue.” Nietzsche .
accused him of demonstrating by sophisticated and obscure arguments
that popular prejudices are right while the scientists are wrong. We
appreciated in Poincare just what was different from Kant. We agreed
with Abel Bey’s characterization of Poincare’s contribution as a “new
positivism” which was a definite improvement over the positivism of
Comte and Mill. Bey wrote:

The new positivism certainly has its origin in the positivism of Comte,
of Taine and Mill . . . It is rejuvenated but has preserved the great direc-
tive ideas from its previous stage: the relativism and empiricism of our
knowledge. But it stresses . . . the idea of experimental categories which
are required by science as a central necessity . . . Positivism is renewed by'^
building a new rationalism upon the criticism of traditional rationalism inj
the second half of the nineteenth century . . . What was lacking in Comte’s
or Mill’s positivism . . . was their . . . failure to have established in a ,
new form a theory of categories. Objective experience is not something which ^
is outside and independent of our minds. Objective experience and mind are f' ,
functions of each other, imply each other, and exist by virtue of each other.

modern science and its philosophy

‘ c

To say that the relations between physical objects derive from the nature of
these objects and to say that these relations are constructed by our minds
are two artificial theories ... _

Our experience is a system, a relation of relations. The relation is the I
given.®’

5. Mach, Poincari and Lanin

^ Chapter 1 of the present book is written in the spirit of this new
positivism. Poincare claimed that the general laws of science— the law
of inertia, the principle of conservation of energy, etc.— are neither state-
ments about facts which can be checked by experiments, nor a priori
statements w'hich necessarily emanate from the organization of human
mind. They are rather arbitrary conventions about how to use some
words or expressions. In this chapter Poincare’s basic tenets are applied
to the law of causality.

I started from Hume’s formulation of this law: When a state A of a
system is followed one time by a state B, every time that A recurs it is
followed again by B. I analyzed this formulation in a way that is sim-
ilar to Poincare’s analysis of the general principles of science. I put the
question: How do we know when the state A has recurred? There is
no exact method except to investigate whether it is followed by B,
Hence the law of causality is not a statement about observable physical
facts but a definition of the expression, “the state A has recurred.”

When I first published this paper ( 1907) it aroused a certain amaze-
ment among scientists. Among the comments were those of two men
of world- wide fame, although in different fields: Einstein and Lenin.
Einstein’s letter was my first personal contact with him. He approved
the logic of my argument, but he objected that it demonstrates only
that there is a conventional element in the law of causality and not that
it is merely a convention or definition. He agreed with me that, what-
ever may happen in nature, one can never prove that a violation of the
law of causality has taken place. One can always introduce by con-
vention a terminology by which this law is saved. But it could happen
that in this way our language and terminology might become highly
complicated and cumbersome. What is not conventional in the law of
® Ibid., pp. 392 S.

historical background

» y

‘ causalit;^ is the fact that we can save this law by using a relatively
simple terminology: we are sure that a state A has recurred when a
small number of state variables have the same values that they had at
the start. This “simplicity of nature” is the observable fact which can-
not be reduced to a convention on how to use some words. These re-
marks had a great influence on my thought on the future course of the
philosophy of science. I realized that Poincare’s conventionalism needs
qualifications. One has to distinguish between what is logically pos-
sible and what is helpful in empirical science. In other words, logic
needs a drop of pragmatic oil.

Lenin’s comment was rather unfavorable. In his book “Materialism
and Empiriocriticism” (we would call it today “Materialism and Posi-
tivism”) he maintains that, “as a Kantian,” I “rejoiced” to be able to
give support to Kant’s idealism by the “most modern philosophy of sci-
ence.” From my reference to the relations between Poincar^ and Kant .
he drew the conclusion that I tried to make use of Poincar^ in the serv-
ice of idealistic philosophy and that, therefore, this paper had an anti-
materialistic and reactionary tendency. Lenin’s book did not come to
my attention before the early twenties. Then, however, it stimulated
me to think over more carefully the relation between Poincar4 and
Kant, between positivism and ideah'sm and, particularly, to investigate
the role that metaphysical interpretations of scientific theories have
played in support of political and religious philosophies.

However, during the interval ( 1907-1917) between writing the first
and second chapters of the present book, my interest was directed
mainly toward any possible advance in the logic of science. I was con-
vinced that the solution must be sought by starting from the ideas of
such men as Mach and Poincar6.'

At first glance these two authors seemed to contradict each other
flagrantly. I soon realized that any advance in the philosophy of sci-
ence would consist in setting up a theory in which the views of Mach
and of Poincare would be two special aspects of one more general view.

To summarize these two theories in a single sentence, one might say:
According to Mach the general principles of science are abbreviated
economical descriptions of observed facts; according to Poincare they

modern science and its philosophy

are free creations of the human mind which do not tell anything about*
observed facts. The attempt to integrate the two concepts into one co- '
herent system was the origin of what was later called logical empiri- j
cism.

6. D. Hilbert's New Foundations of Geometry

, The traditional presentation of physical theories frequently consists
of a system of statements in which descriptions of observations are
mixed with mathematical considerations in such a way that sometimes
one cannot distinguish clearly which is which. It is Poincare’s great
merit to have stressed that one part of every physical theory is a set of
arbitrary axioms and logical conclusions drawn from these axioms.
These axioms are relations between signs, which may be words or alge-
braic symbols; the important point is that the conclusions that we draw
from these axioms are not dependent upon the meanings of these sym-
bols. Hence this part of a theory is purely conventional in the sense
of Poincare. It does not say anything about observable facts, but only
leads to hypothetical statements of the following type: “If the axioms
of this system are true, then the following propositions are also true,”
or still more exactly speaking: “If there is a group of relations between
these symbols, there are also some other relations between the same
symbols.” This state of affairs is often described by saying that the
system of principles and conclusions describes not a content but a
structure. Hence, this system is occasionally referred to as the struc-
tural system.

The simplest example is geometry. It is the first example in the his-
tory of science of a logical system that claims to make statements about
facts in the observable world as well. Geometry did not proceed ac-
cording to the pattern adopted by the older positivists like Hume,
Comte, or Mill. It did not collect facts and draw conclusions from
these observations. Instead, it built up a system of axioms which were
statements containing abstract terms like “point,” “straight line,” “inter-
section.” Conclusions from these axioms can actually be dravm without
knowing the meaning of these terms. In the textbooks of geometry that
were written in accordance with the tradition laid down by Euclid,

historical background

'such tevns as “straight line” or “intersection” seemed to have a “mean-
ing” in the same sense as the words “table” or “horse” have a meaning,
except that the geometric concepts were supposed to be the names of
“idealized” physical objects.

After the turn of the century, however, David Hilbert started a
purge of the foundations of geometry and set up a clear-cut and con-
sistent system of axioms. He stressed that such concepts as “point” ^r
“straight line” have no meaning besides the one defined by the axioms.
The axioms are “implicit definitions” of the geometric concepts. For
Hilbert, as for Poincare, the axioms were conventions about the use of
the geometric terms. In this way Hilbert made a significant contribu-
tion to the “new positivism.” He restricted himself, however, to the in-
vestigation of the structural system and did not discuss, as Foincar4
did, the relation of the geometric axioms to our experience or our sense
observations. The propositions that are derived from the axioms cannot
contain any word besides the symbols contained in the axioms. But
these symbols have no meaning in the physical world. The great asset
of this method is that conclusions can be drawn without being affected
by the vagueness of terms that describe our actual observations, like
“red,” "blue,” “warm,” “sweet.” This method of geometry became the
method of the mathematical physics of the nineteenth century. Heat,
electricity, and light were described by systems of principles that con-
sisted not of observational terms but of abstract symbols. However, the
symbols occurring in the axioms and propositions, of geometry as well
as of mathematical physics, can be linked to observable facts in a brief
and easily understandable way; for example, the straightness of a line
can be checked approximately by the edge of a rigid table, or a vol-
ume or a temperature can be measured by simple physical methods.

7. The New Positivism and P. Duhem's "Thomism''

The axiomatic or structural system, including its conclusions, is
merely an arbitrary convention if the purely logical viewpoint is main-
tained without going into the physical interpretation. It was clear to
, Poincar^ that the structiural system is logically arbitrary because it can-
not be demonstrated by logical means. It is not psychologically arbi-

modern science and its pniiosopny

trary, however, because in practice we construct only those syst^s that '
can be interpreted in terms of physical facts and that are therefore help-
ful for the formulation of natural laws.

If this line of reasoning is followed, we can see, in a perfunctory
way at least, how Mach’s and Poincare’s ideas about the general prin-
ciples of science can be integrated. The axiomatic system, the set of
relations between symbols, is a product of our free imagination; it is
arbitrary. But if the concepts occurring in it are interpreted or identi-
fied with some observational conceptions, our axiomatic system, if well
chosen, becomes an economical description of observational facts.

Now the presentation of the law of causality as an arbitrary con-
vention (Chapter 1) can be freed of its paradoxical appearance. The
law of causality, as a part of an axiomatic system, is an arbitrary con-
vention about the use of terms like “the recurrence of a state of a sys-
tem,” but if interpreted physically it becomes a statement about ob-
servable facts. In this way, the philosophy of Mach could be integrated
into the "new positivism” of men like Hemd Poincare, Abel Hey, and
Pierre Duhem. The connection between the new positivism and the
old teaching of Hume and Comte is the requirement that all abstract
terms of science— such as force, energy, mass— must be interpreted in
terms of sense observations. Exactly speaking, every statement in
which these abstract terms occur must be interpreted as a statement
about observational facts. Mach formulated this requirement by say-
ing that all scientific statements are statements about sense ob-
servations.

Mach’s requirements have frequently been misinterpreted. Some
authors considered them a kind of subjective idealism, meaning that
the world consists of sense data only. Others considered them a kind
of skepticism or agnosticism, meaning that man cannot know anything
about the true or real world; man and man-made science can tell us
only about our sense observations, while the objective reality will be
eternally unknown to human intelligence. In this interpretation science
would be purely subjective, a collection of statements about subjective
sense impressions. This misinterpretation had its source in traditional
philosophy, according to which science and philosophy must find the

historical background

idden ti;pasure of truth behind appearances. All the various systems
■ traditional philosophy seeking objective reality behind appearances
ere opposed to Mach’s philosophy. Moreover, a great many scientists
Lsliked the idea that the statements of science do not describe the
sal world but are only statements about our sense observations, with-
it objective significance.

The property of the structural system of not telling us anything
lOut the world of observable physical facts was particularly empha-
zed by the French scientist, philosopher, and historian, Pierre Duhem.
is writings exerted a strong infiuence upon our group and, particu-
rly, upon my own thinking. By studying Duhem thoroughly we
lined a more subtle understanding of the relations among science,
etaphysics, and religion than has been customary among empiricists,
uhem says, much as Mach had done,

A theory of physics is not an explanation; it is a system of mathematical
opositions deduced from a small number of principles the aim of which is
represent as simply, as completely, and as exactly as possible, a group of
perimenlal laws.*

This formulation is a great step on the way toward an integration
Mach and Poincar4. Duhem understood very well that no single
•oposition of a physical theory can be said to be verified by a specific
:periment. The theory as a whole is verified by the whole body of ex-
jrimental facts. As Duhem put it.

The experimentum crucis is impossible in physics.'
e says again;

The watchmaker to whom one gives a watch that does not run will take it
[ apart and will examine each of the pieces until he finds out which one
damaged. The physician to whom one presents a patient cannot dissect
m to establish the diagnosis. He has to guess the seat of the illness by
amining the effect on the whole body. The physicist resembles a doctor,
)t a watchmaker.*

*P. Duhem, ThSotle physique; son objet—son structure (Paris, 1906), p. 24.
‘Ibid., p. 285.

*P. Duhem, "Quelques reflexions au sujet de la physique experimentale,”
ivue des questions sdentifiques 36, 179 (1897).

modern science and Its philosophy

And elsewhere: »

- The experimental verifications are not the basis of the theory, but its
culmination.

One notes how far Duhem has proceeded on the way from Mach’s con-
ception of a physical theory to the conception which was later advo-
cated by logical empiricism.

Duhem, however, was also, from another angle, a great influence
upon the philosophy of our group. He believed, like Mach, that an
“explanation” that would be distinct from “economical description”
would require an excursion into metaphysics. He says.

If the object of physical theories is to explain experimental laws, physical
theory is not an autonomous science; it is subordinated to metaphysics.

Although he was convinced that physics cannot provide an explanation
of experimental laws, he did not mean to say that no explanation is pos-
sible.

In seeking to stress the distinction between physics and metaphysics I do
not mean to disdain either of these sciences, and I think to facilitate their
accord much better than if I had confounded the object and the method of
the former with the object and the method of the latter . . . The knowledge
that metaphysics gives us of things is more intimate, more profound than
that which is furnished by physics; it therefore surpasses the latter in
excellence.^

As a matter of fact, Duhem was an advocate of Aristotelian and Thom-
istic metaphysics and a faithful believer in the whole of Catholic the-
ology. When I noted this merging of the most advanced type of “new
positivism” with Thomistic metaphysics into one coherent system it im-
pressed me strongly. Duhem interpreted on the basis of this hybrid
philosophy the historic conflict between the Roman Church and the
Copemican system.

Although our group did not follow Duhem’s metaphysical predilec-
tion, his doctrine became for us a frame of reference to which we could

’’ P. Duhem, “Physique et metaphysique,” Revue des questions scientifiques 36,
55 (1897).

historical background

relate all 4he conflicts that have raged between science and religion
and, more generally, between science and political ideologies.

8. E. Mgch as a Philosopher of "Enlrghtenment''

Despite the aversion toward Mach that had been particularly notice-
able among the German scientists and philosophers, he exerted a re-
markable attraction for some groups of scientists as well as of philos- .
ophers. However, the hostile reaction against him was of great intensity.
Disputes about him have been repeated again and again at gatherings
of scientists, the conflict of opinions has always been intense, and the
discussions have frequently had an emotional flavor.

Ernst Mach died in 1917, the year in which the Soviet government
seized the power in Russia. Few among the European and American
scientists realized at the time that the new ruler of Russia had pub-
lished a book ten years previously in which he branded “Machism”
as a reactionary philosophy. This book laid the foundation for a pe-
culiar situation in the new Russia by making Mach a permanent target
of attack. He was accused of agnosticism, subjectivism, and relativism.
It was alleged that Mach had denied that science could know anything
about the objective world. In this way, it seemed, the door was opened
to other ways of finding the truth, particularly to the ways of traditional
religion. It is interesting and amazing that Lenin denounced Machism
by the same argument which has been used by advocates of physical
realism among European and American scientists.

In the year of Mach’s death (1917), 1 wrote Chapter 2 of the pres-
ent book. Its purpose was the investigation of the value of Mach’s
philosophy of science for the future development of science and of
human thought in general. Mach’s philosophy is presented in such a
way that those features are stressed that will survive him and remain
essential parts of any future philosophy of science. This means in par-
ticular that Mach is judged from the viewpoint of the “new positivism”
of men like Poincar6 and Duhem. Mach’s philosophy is described and
characterized with respect to its place in the history of human thought
at the start of the twentieth century. It is likened to the philosophy of
the Enlightenment in the eighteenth century. Mach analyzed the

modern science and its philosophy

fundamental concepts of nineteenth-century physics, such as»mass and
force, and made clear that all statements containing these words can be
interpreted as statements about sense observations. Then concepts like
these do not denote entities of a hidden real world behind the appear-
ances, but are “auxiliary concepts” by which statements about observa-
tions can be expressed in a more convenient and practical way. As the
auxiliary concepts of nineteenth-century science were mainly concepts
of mechanistic physics, Mach’s analysis was to a certain extent a de-
bunking of mechanistic science as a system of statements about phys-
ical reality. Nonetheless, Mach had no special bias against the mecha-
nistic terminology that would imbue him with a particularly antimate-
rialistic tendency. He tried to debunk all types of auxiliary concept
in so far as they pretended to describe ontological realities or meta-
physical entities. I illustrated this function of Mach’s philosophy as a
philosophy of enlightenment appropriate to the turn of the century by
pointing out similarities between Mach and Nietzsche. The great mass
of writing about Nietzsche has largely overlooked the fact that he was
a philosopher of enlightenment in his acute analysis of the auxiliary
concepts of contemporary idealistic philosophy.

The years after 1917 saw, as has been mentioned, the estab-
lishment of Soviet power in Russia, the end of World War I, and the
founding of new democracies in Central Europe, such as the Austrian,
Czechoslovakian, and Polish republics. The event that had the greatest
bearing at this time on the development of the philosophy of science,
however, was the new general theory of relativity advanced by Einstein
after 1916. In this theory Einstein derived his laws of motion and laws
of the gravitational field from very general and abstract principles, the
principles of equivalence and of relativity. His principles and laws were
cormections between abstract symbols; the general space time co-
ordinates and the ten potentials of the gravitational field. This theory
seemed to be an excellent example of the way in which a scientific
theory is built up according to the ideas of the new positivism. The
symbolic or structural system is neatly developed and is sharply sepa-
rated from the observational facts that are to be embraced. Then the
system must be interpreted, and the prediction of facts that are ob-

historical background

servable ipust be made and the predictions verified by observation.
There were three specific observational facts that were predicted: the
bending of light rays and the red shift of spectral lines in a gravitational
field, and the advance of the perihelion of Mercury.

9. A. Einstein's New Concept of Physical Science

However, if we compare Einstein’s theory with previous physical
theories, we note a certain difference in structure. It is after all only a
difference in degree, but it directs our attention to a considerable
change in the conception of physical theory.

Whatever conclusions may be drawn from them, Einstein’s funda-
mental laws will describe motions in terms of the general space-time
coordinates. Before the results of his theory can be verified by observa-
tion, it is necessary to know how statements about these general co-
ordinates can be expressed in terms of observational facts. In traditional
Newtonian physics, spatial coordinates and time intervals could be de-
termined by the traditional methods of measuring length and time, by
using yardsticks and clocks. However, the general coordinates in Ein-
stein’s theory are quantities that define the positions and motions of
moving particles with respect to systems of reference that can possess
all sorts of deformations, with variable rates of deformation at every
point. No rigid and defined system of reference for space and time
measurement is given as a general basis for the definition of the space
and time coordinates. The methods of measurement must be developed
along with the ccnclusions from the principles of the theory. What is
the bearing of these facts upon our general conception of the structure
of a scientific theory?

In nineteenth-century physics the translations of statements that
contain abstract symbols of the theory— mass, distance, time interval,
and the like— into observational facts did not cause much trouble. It
was taken for granted that the straightness of a hne, the temperature of
a body, or the velocity of a motion could be measured. At least, it was
not suspected that there was any difficulty in assuming that such meas-
urements are possible. In Einstein’s general theory of relativity, how-
ever, the description of the operations by which these quantities could

modern science and its philosophy

be measured becomes a serious and complex task; it becomeg an essen-
tial part of the theory. These descriptions of the operations by which
abstract symbols, such as the general space-time coordinates, are con-
nected with observational facts are called today “operational defini-
tions,” according to a terminology suggested by P. W. Bridgman.®

As early as 1905, in his restricted theory of relativity, Einstein was
well aware that the “operational definitions” are an essential part of his
theory. Later he described the decisive alterations that were brought
about by his new physical principles in the conception of a physical
theory by stressing the fact that the connection between the symbols
of the theory and the observational facts following from them is much
longer, much more complex, and much more difficult to deal with than
the connection assumed by nineteenth-century physics, to say nothing
of the physics of the seventeenth and eighteenth centuries. The altera-
tion brought about in the general conception of a scientific theory was
a greater emphasis on the gap between the structural system and the
experimental confirmation. Advancing a new theory now involved two
tasks, both of which required great creative power: the invention of a
structural system, and the working out of operational definitions for its
symbols.

However, the great new idea in every new physical theory, accord-
ing to Einstein, was the creation of the structural system. In this sense
a physical theory describes “the structure of the world.” This way of
speaking could easily be interpreted as meaning that the symbols,
which are the building stones of the structure, are also the “real build-
ing stones” of the universe and that the structure of the symbolic sys-
tem is “the real structure of the world." Following Einsteins ovra in-
terpretation of his conceptions, statements like “the theory describes
the real structure of the world” mean that appropriate operational defi-
nitions enable us to derive from the symbolic system observational facts
that check with our actual observations. Hence, the conception of phys-
ics advocated by the new positivism of Poincar6 is altered by Einstein’s
conception in such a way that a theory remains an economical descrip-

®P. W. Bridgman, The Logic of Modem Physics (New York; Macmillan,
1927 ).

historical background

tion of facts by means of a structure and operational definitions.. How-
ever, the connection between the symbols and the observational fact is
not so simple as was anticipated.

10. Geometry and Experience

.The old problem of the relation between reasoning and experience
in geometry was satisfactorily solved by Einstein’s theory? Even the
advocates of a new positivism, like Poincare and Duhem, left a feeling
of uncertainly concerning the actual position of geometry between the
domains of logic and experience. One might even say that they left a
feeling of uneasiness. J’oincare made it clear that geometry itself as a
logical system says nothing about the physical world. From the view-
point of physics, or of empirical science in general, this logical system
can be judged only as a practical tool which can be used for a descrip-
tion of the physical world. This procedure may be easy or difficult,
simple or comphcated. By using Einstein’s theory, a description of mo-
tions is obtained in terms of spatial and temporal coordinates that are
measured by the reading of yardsticks and clocks. However, these in-
struments, and therefore their readings, are affected by the same gravi-
tational field that is responsible for the motion. An important conse-
quence is that the distances between different points in space follow
the axioms and propositions of Euclidean geometry only if the field of
force is almost negligible. If we have to consider “strong” fields, the dis-
tances between points no longer fit the rules of Euclidean geometry.
This means, for instance, that the sum of the angles in a rectilinear tri-
angle is no longer exactly equal to two right angles. The departure from
two right angles is the greater the larger the area of the triangle and
the stronger the field of gravitation. In order to give to these statements
a physical meaning we assume tacitly that “straight lines” are defined
by the traditional technologic procedures by which straight edges are
produced on rigid bodies, such as a bar of steel^

This means in ordinary geometrical parlance that Euclidean geome-
try is valid only if the field of gravitation is negligible and if the areas
of triangles are small. Generally the laws that determine the relation
between the measured distances will be those of non-Euclidean geome-

modern science ond its philosophy

try. ^oincar^ and his immediate followers used to say that it is a con-
vention whether one accepts Euclidean or non-Euclidean geometry.
Actually this statement means only that we can build up structural
systems of two types: Euclidean and non-Euclidean. As a structural or
axiomatic system both are equally acceptable. If traditional methods
of measurement are used— that is, if length and time are defined in
terms of operations with rigid yardsticks and orthodox clocks— the fact
must be considered that the instruments of measurement are affected
by gravitational fields and therefore that the results of measurement,
too, are affected. For every specific field of gravitation, the theory
yields a specific influence on the yardsticks and clocks and therefore
upon the results of measurement. By considering this influence “opera-
tional definitions” can be formulated. The statements of mechanics
now become statements about the results of actual measurements or
about actual observations. They are therefore no longer arbitrary. If
they are checked, they will be found to be either true or false. In a
gravitational field the yardsticks and clocks will be affected in such
a way that the results of measurements follow non-Euclidean rather
than Euclidean geometr}^

In 1921, Einstein gave a lecture at the Academy of Sciences in
Berhn with the title “Geometry and Experience,” ® in which he sum-
marized in a conclusive way the place of reasoning and experience in
geometry. Recording to Einstein, geometry can be either a structural
system with arbitrary axioms or a physical theory. In the first case
the conclusions of geometry are certain but do not tell us anything
about the world of experience; in the second case the propositions of
geometry can be checked by experiment and are as certain or uncertain
as are any statements of physics or, for that matter, of any empirical
science.]

By Einstein’s argument it was demonstrated with great lucidity that
there is no statement in geometry that is derived by reasoning without
sense observations and that at the same time tells us something about
the external world. Such geometric propositions, however, had been

” An English translation of this lecture appeared in A. Einstein, Sidelights on
Relatioity (London: Methuen, 1022).

historical background

considered the most conspicuous examples of^ssertions about the ex-
ternal world that are derived from pure reasoning. If the statements
of geometry do not have this property, then the scientific basis of
traditional metaphysics has disappeared. The cause of positivism
against metaphysics has won a major battlq/

11. NeO'Kantianism and Neo«Thom!sm

When Einstein had cleared up the foundations of geometry, the
believers in scientific metaphysics were put on the spot; they were
deprived of their best example of the existence of metaphysical asser-
tions in science itself.

Cam schools of traditional philosophy have more or less one belief in
common: we can make general statements about facts of the external
world with such certainty that they will never be refuted by any
advance in science. For Aristotle such statements were the
’ " of Greek astronomy, for Kant they were Newton’s principles
Both the Aristotelians and the Kantians of the nineteenth
and twentieth centuries agreed that the validity of Euclidean geome-
try had been established forever. The only difference was that for one
school the doctrine that was believed to prevail forever was Aristotle’s
physics, while the other, more modem, school permitted the pursuance
of the advance of science up to Newtot^ Each philosophical creed
petrified the state of physics that prevailed at its time.

^When Einstein demonstrated Ae possibility or even the plausibility
that Euclidean geometry might be wrong he produced a catastrophic
effect upon all the schools of traditional philosophy. The metaphysical
schools of the Aristotelian and the Kantian types lost their basis in
science,J^o meet this situation two attitudes have developed within
these schools. To borrow a terminology from theology, we may call
them the fundamentalist and the modernist attitudes. The first group
maintain ed bluntly and boldly that scientists were just wrong. They
were specialists and not able to reason correctly because of their lack
of metaphysical training.

The modernists are found in the camps of neo- Aristotelians (mostly
called neo-Thomists) and of the neo-Kanti^s. They admitted that

modern science and its philosophy

Euclidean geometry might be wrong. This was, according to these
schools, the truth, but “not the whole truth." From the viewpoint of
science proper, they have accepted fully the conception of geometry
and physics advanced by the new positivism. But in the background of
their teaching on geometry and physics there is a hint of a more pro-
found wisdom which is presented in terms of Aristotelian or Kantian
metaphysics.'^As an example of neo-Thomism we may consider the
works of J. Maritain, particularly his book, “The Degrees of Knowl-
edge.” An example of neo-Kantianism is the writing of Ernst Cassirer,
particularly his books on the “Theory of Relativity” and on “Determi-
nism and Indeterminism in Modem Physics.” The latter one is dis-
cussed in Chapter 9 of the present book, ^his metaphysical back-
ground, according to these authors, has no relevance for science proper;
it is separated by airtight walls from the domain of scientific dis-
course. In this way science became autonomous with respect to meta-
physics, but the validity of the metaphysical assertions in the back-
ground could not be checked by any experimental test. These assertions
became more or less a tautological system of propositions, like pure
mathematics or formal logic.“ However, this did not exclude the
possibility that this metaphysical background may provide some satis-
faction to readers or listeners.^s a matter of fact, the metaphysical dis-
course has been usually couched in language that has evoked a pleasant
resonance in people’s minds. This kind of language has been in use to
present cherished types of science, ethics, or religion. If we disregard
temporarily this background there is a large common ground between
neo-Thomism, neo-Kantianism, and the new positivism. In extreme
cases this common ground may be so extensive that one can read
himdreds of pages of a neo-Thomist or a neo-Kantian without recog-
nizing that he is not a positivist of the new type. The most outstanding

“ J. Maritain, Distinguer pour unit, ou les degris du savoir (Paris: Brouwer,
1935); English translation by B. Wall and M. R. Adamson (New York: Scribner,
1938).

Cassirer, Zur Einsteinschen relativitiUstheoric (Berlin: Cassirer, 1921).

i*E. Cassirer, Determinismus und Indeterminismus in der modemen Physik
. . . (Goteborg: Elanders, 1937).

“C. W. Morris, Signs, .Language, and BehaviOT (New York: Frentice-Hall,
1940), pp. 175 ff.

historical background

exampte is the French physicist and philosopher, Pierre Duhem, whom
we mentioned above. His writings are among the most valuable con-
tributions of the new positivism. He was warmly recommended by
Ernst Mach as a positivist. Many scientists were never aware that
Duhem’s background was straight Aristotelian or rather Thomistic
metaphysics.

12. "New Wine into New Bottlei"

The neo-Thomist and neo-Kantian schools reacted to the revolu-
tionary changes that have arisen in science since the turn of the
century by establishing a kind of “iron curtain” between science and
philosophy. But none of these schools, and, as a matter of fact, none
of the schools of traditional philosophy, of the idealistic or realistic
type, were able to make a valuable contribution toward integrating
the new science of the twentieth century into the general framework
of human thought. From the viewpoint of intellectual history it is fair
to say that the neo-Thomist and neo-Kantian schools have contributed,
in a way, to the advance of scientific thought. They have helped to
disintegrate the traditional systems to such a point that the remaining
parts of the structure could easily merge with the new philosophy that
would eventually arise on the basis of a new science. •

[^Immediately after Einstein had published his general theory of
relativity (1917), in which he advanced his new physics in full gen-
erality, writings appeared that did not attempt to integrate the new
physics into traditional philosophy but to build up a new philosophy
on the basis of that new science^ These writings did not follow the
reaction of traditional philosophy— of either the fundamentalist or the
modernist types— to the new science. Theirs was a radical reaction in
accordance with the words of the gospel:

No man putteth new wine into old bottles; else tbe new wine will burst
the bottles, and be spilled, and the bottles shall perish. But new wine must
be put into new bottles; and both are preserved. No man also having drunk
old wine straightway desireth new: for he saith. The old is better.

Tbe old bottles were the patterns of traditional philosophy and the
new wine was twentietii-century science. A ^up of men went in for

modern science and its philosophy

new bottles. They did not borrow the framework of Thoiristic or
Kantian metaphysics but they borrowed a pattern that had grown up
in the soil of modern science, the pattern of the “new positivism.”
While men like Poincare and Duhem had used this pattern for strictly
domestic consumption, to clear up their own back yard, the foundations
of science, the new men who emerged after 1917 ventured to build up
a new philosophy that was expected to replace the traditional systems
of the Aristotelian or Kantian type.

The new movement started about the time when the first world
war ended (1918). New democratic republics were established in
Central Europe: Austria, Czechoslovakia, Poland, and the Weimar
experiment in Germany. They offered a favorable soil for the evolu-
tion of a scientific world conception. A similar situation seemed to arise
in Russia after the overthrow of the Czarist regime (1917). It is inter-
esting to note how the turn from the democratic start to the establish-
ment of a new authoritarianism was accompanied by a turn from the
philosophy of the new positivism to a philosophy which was nearer
to the Aristotelian and Kantian tradition.

The first peak of the Central European movement toward a scientific
world conception was reached about 1920. We can characterize it by

• three books; M. Schlick, “General Theory of Knowledge”” (1918);

• H. Reichenbach, “Theory of Relativity and Cognition a priori” “

1^(1920); and L. Wittgenstein, Tractatus Logico-Philosophicus (1921).'“

The link between these books and Einstein’s theory is M. Schlick’s
small book "Space and Time in Contemporary Physics” (1917),” in
which the author attempts an integration of the new positivism with
the ideas that have grown out of Einstein’s new science.

”M. Schlick, Allgemeine Erkenntnislehre (Berlin: Springer, 1918; ed. 2,
1925).

H. Reichenbach, Relatlvitdtstheorie und Erkenntnis apriori (Berlin: Springer,
1920).

'*L, Wittgenstein, Tractatus hgico-philosophicus (London: Paul, Trench,
Trubner; New York: Harcourt, Brace, 1922); German and English on opposite
pages;

M. Schlick, Raum und Zeit in der gegenwartigen Fhysik, . . . (Berlin:
Springer, ed. 3, 1920); English translation by H. L. Brose (Oxford: Clarendon
Press; New York: Oxford University Press, 1920).

historical background

13. M. Schlick's New Criterion of Truth

The views of the new positivism just before Schlick entered the
picture are presented in Chapter 2, which was written in the same
year as Schlick’s “Space and Time.” In this chapter la distinction is
made between observational concepts— red, warm, . . .—and auxiliary
concepts— force, electric charge, ... All statements of science that
contain auxiliary concepts are translatable into statements containing
observational concepts only. The expression “auxiliary concept” was
often interpreted as meaning that by words like “force,” electric
charge,” “potential,” no “element of reality” is denoted. Schlick, how-
ever, stresses that the usefulness of a statement in science depends
only upon whether this statement can be checked by sense observa-
tions. In other words, a scientific theory must consist of such principles"^
that statements containing observational concepts only can be logically
derived from them. It is irrelevant whether the concepts in the theory
itself are “observational concepts” or “auxiliary concepts.”

Schlick says:

There is no argument whatsoever to force us to state that only the in-
tuitional elements [i.e., observational concepts], colors, tones, etc., exist in
the world. We might just as well assume that elements or qualities which
cannot be directly experienced also exist. These can likewise be termed
“real,” whether they be comparable with intuitional ones or not. For ex-
ample, electric forces can just as well signify elements of reality as colors and
tones. They are measurable, and there is no reason why epistemology should
reject the criterion for reality which is used in physics.^®

To say that electric forces are “measurable” means that from statements
of the form, “At this point of space acts an electric force of one hundred
grams,” statements can be derived about the deviation of a pointer
from its coincidence with a certain mark of a scale. This means, how-
ever, statements about direct sense observation. It does not matter
whether the words in a statement denote observational concepts or
auxiliary concepts provided that results can be derived that contain
only observational (intuitional) terms.

“ffifcl., p. 84.

modern science and its philosophy

For Otherwise no measurement would be possible. Therefore, the
“operational definitions”— which link auxiliary and observational con-
cepts— are an indispensable part of every theory. This point is very
important for integrating Einstein’s new science into the scheme
of new positivism. Now, one can, without any trouble, introduce terms
like “four-dimensional space” or “curved space” into physics. These
concepts are as legitimate as three-dimensional space and Euclidean
geometry. We have only to make sure that our systems contain the
rules by which, from the facts of the theory, only observational con-
cepts can be derived.

From this characterization of scientific theories Schlick proceeds
to an even more radical departure from traditional philosophy. He
starts from the method that is generally used in science to check the
“truth” of a theory. One considers, for example, the electric charge of
an electron, which, according to the theory, should have a constant
numerical value. Then one derives from the theory by a chain of
conclusions the result that “the charge of the electron is 4.7 X 10~’“
electrostatic units.” Then one tries to find, on the basis of the same
theory, a second chain of conclusions by which the numerical value
of the charge of the electron can be derived. If this value is different
from the first one, we say that our theory is “not true.” If we obtain
the same value as by the first method, we say that our theory may be
true or “is confirmed.” The "degree of confirmation” is the higher the
more independent chains we can find that lead to the same numerical
value for the charge and for other concepts of the theory.

This criterion of truth can also be formulated in a more general
way. The symbols of the theory (observational or auxiliary concepts)
are the state variables by means of which the course of events in the
physical world— the facts of the world— can be described. Every specific
state of the world is defined by specific numerical values which are
assigned to these variables. Some of them, like the charge of the
electron, are constants. Others, like the coordinates of an electron, are
variables. As we learned by the example of the charge of the electron,
we can make use of the theory to calculate these numerical values.
This means that the theory indicates the facts of the world. If we

hstorical background

obtained from two difiFerent chains of conclusions different numerical
values for a symbol which, according to the theory, should be constant,
then one and the same theory would indicate two incompatible facts.
Such a theory would be useless.

From these remarks one will understand fairly well Schlick’s
criterion for the “truth” of a theory. He says:

/Every theory is composed of a network of conceptions and judgments,
and is correct or true if the system of judgments indicates the world of facts
uniquely}^

If a theory yields two different values for the charge of the electron, the
correspondence between the theory (concepts and judgments) and
the facts would not be a unique correspondence.

On the other hand, no harm is done if different theories indicate one
and the same world of facts. In the direction from the facts to the
theory no uniqueness is required of “true” theory. Schlick says:

It is, however, possible to indicate identically the same set of facts by
means of various systems of judgments; and consequently there can be
various theories in which the criterion of truth [unique correspondence] is
equally well satisfied . . . They are merely different systems of symbols,
which are allocated to the same objective reality.™

14. M. Schlick and H. Relchenbach

From this analysis of scientific theories Schlick proceeded to the
claim that every cognition, in whatever domain of knowledge, is essen-
tially the establishment of a correspondence between the facts of the
world and a system of symbols. Since between these symbols a set of
relations— for example, the axioms of geometry or mechanics— is estab-
lished, an arbitrary correspondence would frequently assign several
worlds of facts to the same set of symbols. Then the cognition is false.
According to Schlick, a cognition is “true” if the correspondence es-
tablished is unique. A system of symbols indicates the facts of the
world uniquely.

“Ibid., p. 86.

“ Loc. cit.

modern science and its philosophy

This conception of cognition and truth was a radical bref.k with
almost all systems of traditional philosophy, according to which cog-
nition meant the finding of a truth that was hidden behind the appear-
ances and could be discovered there by the power of reason, which
the trained philosopher was supposed to possess. According to Schlick,
however, cognition is the establishment of a correspondence; this
means, primarily, building up a system of symbols with relations
among them. Cognition becomes an activity, the construction of a sys-
tem of symbols that has only to fulfill the requirement of uniqueness.
If we start from this conception of cognition, most of the metaphysical
problems that have puzzled generations of philosophers lose their in-
soluble aspect.

Consider, for example, the ancient puzzle whether the world is es-
sentially mind or matter, the answer to which has been the shibboleth
for distinguishing between idealists and materialists. Schlick would
reformulate the problem: Are mental concepts or physical concepts
better suited to build up a system of symbols that could indicate the
world of facts uniquely? The problem loses its yes-or-no character and
becomes a problem of deciding, on grounds of convenience, between
two ways of describing the facts of the world.

Another author who ventured at that time to build up, on the basis
of the “new positivism” and Einsteins new theories, a philosophy of
science that would replace the traditional schools was Hans Reichen-
bach. His most significant books in this line, which to a certain extent
paralleled Schlick’s writings, are the “Theory of Relativity and Cog-
nition a priori” “ and “Axiomatics of the Relativistic Theory of Space
and Time.” ” Reichenbach went in much more for the technical dis-
cussion of physical and philosophical problems than Schlick did. He
approved Schlick s conception of “true cognition,” but he presented it
in a way that was closer to the conception of science advanced by men
like Poincare and Duhem. Reichenbach was perhaps the first one who
formulated explicitly the requirement that every theory in which non-
observational concepts appear contain relations between these abstract

” H. Reichenbach, AxiomaUk der relativistUchen RaurtirZett-lehre ( Braun-
schweig: Vieweg, 1924).

historical background

concepts and observational concepts. He stressed that geometry as an
empirical science must contain, besides the geometric axioms (relations
among geometric concepts), the description of a method whereby the
straightness of a line can be tested experimentally. As the axioms of
geometry and the description of measmrements form a net, we can re-
gard the whole theory as a prescription for coordinating the abstract
concepts of geometry with observational facts. In this sense, Reichen-
bach regarded geometry as a system of “axioms of coordination.” His
criterion of truth was then similar to Schlick’s, namely, that the axioms
of coordination should be unique.

This uniqueness could, as he stressed, be correctly decided only by
observation. On this basis, Reichenbach discussed the question whether
the new philosophy was compatible with the traditional Kantian sys-
tem. Ry Einstein’s new science it was demonstrated that the Euclidean
axioms of coordination may be false. Einstein described definite ex-
periments by which one can test whether the traditional axioms of co-
ordination lead to contradictions. Kant believed that the imiqueness of
Euclid’s system of geometry is founded in the organization of the hu-
man mind, while Reichenbach stressed that it has to be checked by
experience. In the discussion (Secs. S and 4) of the relation of Poin-
care to Kant I made partial use of Reichenbach’s views.

15. L. Wittgenstein and R. Carnap

The work done by Schlick and Reichenbach made a strong impres-
sion upon our Viennese group (Sec. 1). In our search for a scientifically
founded philosophy we were glad to find collaborators who attacked
the task, I would say, from a more professional angle. At that time
(after 1920) Hans Hahn was professor of mathematics at the Uni-
versity of Vienna, Otto Nemath started working for the City of Vienna,
organizing adult education in the social sciences, and I had been since
1912 professor of theoretical physics at the University of Prague in
the new Czechoslovakian Republic. Hahn had started intensive work
with advanced students in the field of symbolic logic and the founda-
tions of mathematics. In 1922, he chose as a basis of their discussions
the new book by L. Wittgenstein, Tractatus^ Logico-Pkilosophicus,^

modern science and its philosophy

These discussions were the germ of many future developmenfs in the
philosophy of science.

Wittgenstein’s book followed in some respects the same line as
Schlick’s and Reichenbach’s. Wittgenstein, who was also of Viennese
origin, was a student of Bertrand Russell, the British logician and
philosopher. He added a new and important component to the integra-
tion performed by Schlick. Without making much use of the tech-
nicalities of symbolic logic, Wittgenstein showed that the new philos-
ophy could be brought into a more perfect and coherent shape with the
aid of the basic ideas of Russell’s logic. Wittgenstein’s formulations
sounded even more straightforward and provoking than Schlick’s,
Reichenbach’s, and even Russell’s. Wittgenstein claimed bluntly that
I the problems of traditional philosophy are merely verbal problems.
Our ordinary language, which has grown up to describe the facts of
everyday life, is not adapted to the task of expressing and answering
problems put to traditional philosophy. If we try to use our ordinary
language in this way, we get into trouble. The real problem is to find
out what one actually can say clearly. The world of facts can be de-
scribed in our ordinary language; therefore, says Wittgenstein, “to
understand a proposition means to know what is the case if it is true.”

This conception of “meaning” and “understanding” is essentially no
different from Schlick’s, Reichenbach’s, or, as a matter of fact, Mach’s,
if we understand Mach as he is interpreted in Chapter 2 of the present
book. Every student of philosophy will also remember C. S. Peirce’ s
conception of “meaning,” and even William James’s, who said that the
meaning of a sentence is its "cash value .”

Wittgenstein’s merit, however, was his precise logical formulation
and his cutting and striking dialectic. His line was later called, quite
adequately, "therapeutical positiv ism.” Hahn became very enthusiastic,
starting a close cooperation of the new men with our Viennese group.
He envisaged the appointment of M. Schlick as a professor of philos-
ophy at the University of Vienna. He met, of course, a stiff resistance
among the adherents of traditional philosophy. But the interest of the
scientists in the philosophical background of science has been tradi-
tionally high at the University of Vienna. Ernst Mach had owed his

historical background

appoinftnent to this predilection and Hahn succeeded in enlisting a
sufficient number of scientists in a drive to carry through Schlick’s ap-
pointment in 1922. In this year a close cooperation between Schlick
and the old Vienna group began. This common work gained a great
deal in intensity and momentum when Schlick persuaded R. Carnap
to move to Vienna in 1926.

Camap gave the new philosophy its “classical” shape. He coined
many of its terms and phrases and endowed it with subtlety and sim-
plicity. In the form created by Camap it became a center of interest
and a target of attack on a large scale.

Schlick and Reichenbach had identified “tme cognition” with a
system of symbols that indicated the world of facts uniquely. Camap
offered an example of such a system in his book “The Logical Stmcture
of the World.” In this book the integration of Mach and Poincare
was actually performed in a coherent system of conspicuous logical
simplicity. Our Viennese group saw in Carnap’s work the synthesis
that we had advocated for many years.

Camap introduced as the elementary concepts of his system im-
mediate sense impressions and the relations of similarity and diversity
between them. The world is to be described by statements that may .
contain any symbols, provided that from them statements can be
logically derived that contain nothing but assertions about similarity
between sense impressions. The “meaning” of a statement in science
would be the sum of all statements about similarity and diversity be-
tween sense impressions that can be derived logically from the state-
ment in question. When I read this book it reminded me strongly of
William James’s pragmatic requirement, that the meaning of any state-
ment is given by its “cash value,” that is, by what it means as a direction*^
for human behavior. I wrote immediately to Camap, "What you advo-
cate is pragmatism.” This was as astonishing to him as it had been to
me. We noticed that our group, which lived in an environment of
idealistic philosophy had eventually reached conclusions by which we
could find kindred spirits beyond the Atlantic in the United States.

From Carnap’s presentation it was clear that a system from which

R. Camap, Der logische Aufbau der WeU (Berlin: Weltkreis-Verlag, 1928).

modern science and its philosophy

one cannot derive results about similarities between sense imj^essions
caimot be a “true cognition.” The statements of traditional metaphysics,
such as those about the existence or nonexistence of the external world,
can obviously not be statements of the required type. For this reason
Carnap said that “metaphysics is meaningless.”

16. O. Neurath's "Index of Prohibited Words"

The men who had expanded the new positivism into a general log-
ical basis of human thought— Schlick and Carnap— came now into per-
sonal contact with the original Viennese group, particularly with Hahn
and Neurath, while my own contact was restricted to the time of the
university vacations. As a result of the developing cooperation the
new philosophy became more and more different from the traditional
German philosophy, to which both Schlick and Carnap were bound
to have some sentimental ties originating from their training at German
universities.

They had demonstrated logically that no scientific metaphysics is
possible because metaphysical statements do not fit into the pattern
that statements must have in order to be called true or false. But the
social scientist Neurath investigated the meaning of metaphysical state-
ments as social phenomena. He insisted with a certain nithlessness that
no formulation should be allowed to slip in that would “give comfort
to the enemy,” even if it would be admissible from the purely logical
viewpoint. The whole original Viennese group was convinced that
the elimination of metaphysics not only was a question of a better
logic but was of great relevance for the social and cultural life. They
were also convinced that the elimination of metaphysics would deprive
the groups that we call today totalitarian of their scientific and philo-
sophic basis and would lay bare the fact that these groups are actually
fighting for special interests of some kind.

In the long thorough and intimate discussions that the Viennese
group had with Schlick and Carnap, the point was made that the new
philosophy must be built up in such a way that no misinterpretation
in favor of metaphysics could occur. We all knew that misinterpreta-

historical background

tions were bound to happen if and when expressions like “real,” “essen-
tial,” “real building stone of the universe,” were used in a loose way.
Neurath even recommended, half jokingly, that an “index of prohibited
words” should be set up. In a monograph “ on the “Foundations of
the Social Sciences” he avoided, as he explicitly states, words like “en-
tity,” “essence,” “mind,” “matter,” “reality,” “thing.”

A well-known example of misinterpretation of this type is the praise
or condemnation of Machs philosophy as a brand of idealism be-
cause his doctrine was often presented as claiming that the “world
consists actually only of sensations.” This was interpreted again as
meaning that the “world is essentially mental.” This interpretation ac-
counts for Lenin’s violent attack on Mach and for the extremely hostile
attitude of the official Soviet philosophy against all doctrines that
traced their origin back to Mach. This holds also for the new positivism
and its generalization as achieved by Schlick, Reichenbach, and Car-
nap.

Perhaps the most striking effect of the cooperation of Schlick
and Carnap with the old Viennese group was the shift to “physicalism”
and to the “unity of science.” Neurath had been particularly eager to
prohibit any establishment of a metaphysical doctrine by a tactic of
infiltration. He suggested that sense data should be dropped as ele-
mentary concepts of the logical structure of the world and replaced
by physical things. Instead of building up the system of human knowl-
edge upon concepts like "red spot” or "feeling of warmth,” one should
use elementary symbols expressing concepts like “rock” or “table,”
and define “redness,” or “warmth” as derived concepts. As the starting
point in sensation had a certain tint of idealism, so the new starting
point had a tint of materialism. Carnap had in his “Logical Structure
of the World” spoken of “methodical materialism” as a possible lan-
guage for his system. But he had come to prefer “phenomenal lan-
guage,” statements in terms of sense impressions. Neurath worked out
a system based on physical things as elementary concepts and called by

^International Encyclopedia of Unified Science (Chicago; University of
Chicago Press, 1938-39), vol. 2, no. 1.

modern science and its philosophy

him “physicalism.” Camap refined Neurath’s physicalism to a®precise
logical structure and even constructed a “physicalistic language” for
the field of psychology.

This transition from a quasi-idealistic to a quasi-materialistic lan-
guage, which took place in our group about 1930, has been misunder-
stood by great many authors. They interpret it as a sudden jump into an
opposite type of philosophy. As a matter of fact, the “jump” was an
expression of our firm belief that the difference between an idealistic
and a materialistic system is logically and scientifically of little im-
portance and that there is actually only a difference of emphasis. The
choice is determined largely by the emotional connotations or, in other
words, by the language in which the pattern of our general culture
is usually described.

17« O. Neuroth and the "Unity of Science Movement"

The second reformulation suggested by Neurath was the char-
acterization of the new movement as a work “towards the unification
of science” or “for the construction of a unified science.” This shift
was for many people surprising too. Schlick and Carnap had stressed
the point that there are no philosophic propositions but that there is a
philosophic activity that consists in the clarification of the statements
of the special sciences. This meant, briefly, that philosophy was to
interpret the abstract and symbolic principles of science as state-
ments about physical things. Frequently, particularly in Great Britain,
the new philosophy has been distinguished from the traditional phi-
losophy as “analytic philosophy” in contrast to “speculative philosophy.”
The work of men like Moore, Russell, or Wittgenstein has been de-
scribed as analytic philosophy.

Our original Viennese group and particularly Neurath were not
satisfied with ascribing to our new philosophical group mainly critical
and analytical objectives. We knew well that man is longing for a
philosophy of integration. If the new philosophy refuses to serve the
cause of integration, a great many people, including even scientists,
would rather return to traditional metaphysics than be restricted to a
purely analytic attitude. As a matter of fact, the traditional goal of

historical background

“philosephy,” through thousands of years of human knowledge, has
been integration.

Neurath pointed out that by Carnap’s analysis the statements of
all sciences, not only physics but also biology and sociology, had been
reduced to statements about physical things or about sense impressions.
The traditional opinion about the individual sciences has, however,
been that the fundamental concepts of biology are essentially different
from those of physics, the concepts of psychology different from those
of biology and so on. Physics, biology, and psychology have to do with
different kinds df “being” and can never be united on the level of
science. Only by introducing metaphysical concepts can one achieve
a unification. If we accept, however, Carnap’s analysis of science, it
follows that all statements of science are of only one type, that is, they
are statements that can be expressed in the “thing language.” Hence, it
must be possible to introduce a unified language for all the sciences and
to create a system of "unified science,” in which the “special sciences”
are merely products of the division of labor. The terminology of the
special sciences is practical for restricted purposes, but no philosophic
implication about unbridgeable gaps can be drawn from the differences
in terminology.

The new philosophy now described its work as the building up of a
unified science. With this goal we returned in some measure to the
classical goal of philosophy as defined by Aristotle. As a matter of fact,
August Comte, the father of positivism, said (1829):

I employ the word “philosophy” in the sense that was given to it by
Aristotle, as denoting the general system of human conceptions.

Our group did not wish to stress die work on analysis in contrast to
the creation of a synthesis. We never regarded the logic and analysis
of science as a goal in itself; we believed strongly that this analysis
is a necessary part of obtaining an unprejudiced ^outlook on life. The
close connection between the positivistic attitude and the unification
of science can be traced back to Ernst Mach himself. In Chapter 3
of the present book I analyze Mach’s philosophy from the viewpoint
of 1938, the one-hundredth anniversary of his birth, and point out to

modern science and its philosophy

what degree the further evolution of positivism was anticiQ^ated in
Mach’s writings.

18. The Vienna Circle

In 1929, we had the feeling that from the cooperation that was
centered in Vienna a definite new type of philosophy had emerged. As
every father likes to show photographs of his baby, we were looking
for means of communication. We wanted to present our brain child
to the world at large, to find out its reaction, and to receive new
stimulation.

We decided first to publish a monograph about our movement,
next, to arrange a meeting, and eventually to get control of a philo-
sophical journal so that we would have a way of getting the contri-
butions of our group printed.

When we prepared the monograph we noticed that our group and
our philosophy had no name. Quite a few people among us disliked
the words "philosophy” and "positivism” and id not want them to
appear in the title. Some disliked all “isms,” foreign or domestic.
Eventually we chose the name “scientific world conception.” Some
of us, particularly Schlick, thought that every reasonable scientist
would agree with our presentation of cognition. Our chosen title
seemed a little dry to Neurath, and he suggested adding “The Vienna
Circle,” because he thought that this name would be reminiscent of
the Viennese waltz, the Vienna woods, and other things on the pleas-
ant side of life. The monograph ’’ was written by Carnap, Hahn, and
Neurath in close cooperation.

Two years later, A. Blumberg and H. Feigl published in the United
States a paper, “Logical positivism; A new movement in European
philosophy,” “ and provided the “scientific world conception” with its
international trade name.

“We chose the term “world conception” (Weltauffassung) in order to avoid
the German word Weltanschauung, which seemed to us loaded with metaphysical
connotations.

Wissenschaftliche Weltauffassung der Wiener Kreis (Wien: A. Wolf, 1929).

“A. Blumberg and H. Feigl, Journal of Philosophy 28, 281 (1931).

historical background

In accord with the historical and cultural inclination of the Vien-
nese group, Neurath was eager to trace the genealogic lineage of our
movement. In the monograph he recorded the following lines:

Positivism and empiricism; Hume, the philosophers of the En-
lightenment, Comte, Mill, Avenarius, Mach.

Scientific method: Helmholtz, Riemann, Mach, Foincar^, Enriques,
Duhem, Boltzmann, Einstein.

Symbolic logic and its application to reality: Leibniz, Peano, Frege,
Schroeder, Russell, Whitehead, Wittgenstein.

Eudaemonistic ethics and positivistic sociology: Epicurus, Hume,
Bentham, Mill, Comte, Feuerbach, Marx, Spencer, Mueller-Lyer,
Popper-Lynkeus, Carl Menger.

A great many misunderstandings have been current about the orig-
inal doctrine of the Vienna Circle, which became the germ of logical
positivism. Again and again philosophers have sought to prove to the
“positivists” that there is a “real world” and that science explores this
real world. In fact, the monograph says: "Something is real if it is a
part of the system of symbols that denotes the world of facts.” A num-
ber of authors have tried to refute “positivism” by showing that there
are also unobservable elements in science that have to be called “real,"
for example, the electron. The quoted passage clearly expresses the
fact that “real” is not regarded as identical with “observable.” We can
state the meaning of the quotation also in slightly different words:
Every symbol denotes something real if this symbol is a part of a^'
system that serves to describe observable facts uniquely.

19. The First Public Meeting

The arrangement of the meeting was not so easy. We wanted to
reach a large audience. The ordinary regular philosophy meetings
followed the traditional lines and would hardly have given us enough
scope. By a happy coincidence I was just in 1929 arranging a meet-
ing of the physicists and mathematicians from the German-speaking
regions in Central Europe. The meeting was to be held in my place
of residence, Prague, the capital of Czechoslovakia. The German

modern science and its philosophy

Physical Society, which was the oiEcial sponsor of this meeting, did
not particularly like the idea of combining this serious scientific meet-
ing with such a foolish thing as philosophy. However, I was the chair-
man of the local committee in Prague and they could not refuse my
serious wish to attach a meeting with the topic, “Epistemology of the
Exact Sciences.” This meeting was to be sponsored by the Ernst Mach
Association, which was the legal organization of the Vienna Circle,
and the Society for Empirical Philosophy, which was organized in
Berlin and followed in general the line of H. Reichenbach. In this way
we provided a nucleus of interested people and hoped that quite a
few mathematicians and physicists who came to Prague for their
meeting would also attend our gathering.

Some scientists wanted to minimize our program and predicted
that we would have no audience from the ranks of the exact scientists.
As a matter of fact, our addresses had a larger audience than papers
on special scientific problems. I had prepared an elaborate paper that
was intended to give the scientists a kind of preview of our ideas and
to prove that the new line in philosophy is the necessary result of the
new trends in physics, particularly the theory of relativity and the
quantum theory. I elaborated the contrast between the “school philos-
ophy,” which sought to preserve the traditional doctrines despite the
new science, and the “scientific world conception,” which wants to
pour the new wine into new bottles. I stressed also the similarity be-
tween the new scientific world conception and the basic ideas of
American pragmatism, particularly those of William James. This lec-
ture is Chapter 4 of the present book.

Some friends cautioned me not to speak too bluntly. The audience,
which consisted mostly of German scientists, knew little of philosophy,
except that they had some sentimental ties to Kantianism. This doc-
trine was regarded in some intellectual quarters as a kind of .substi-
tute for the traditional forms of religion. My wife said to me after the
lecture: ‘Tt was weird to listen. It seemed to me as if the words fell
into the audience like drops into a well so deep that one cannot hear
the drops striking bottom. Everything seemed to vanish without a
trace.”

historical background

Ther# is no doubt that quite a few people in the audience were
shocked hy my blunt statements that modem science is incompatible
with the traditional systems of philosophy. Probably, most of the
scientists had not been accustomed to thinkin g of philosophy and
science as one coherent system of thought. Philosophy had been for
them what the Sunday sermon is for a businessman who is only inter-
ested in profit. Philosophy had been required not to be “tme” but to
give emotional satisfaction.

After the meeting, however, our committee received a great many
letters from scientists who expressed their great satisfaction that an
attempt has been made toward a coherent world conception without ’
contradictions between science and philosophy. We even received
one letter from a professor of philosophy at a German university who
wanted to go on record with his conviction that the remaking of
philosophy, along the lines that we followed at our meeting, is
necessary.

20. M. Schlick Announces a 'Turn in Philosophy"

In the years 1930-31, tliere appeared the first volume of the jour-
nal Erkenntnis (Cognition), which became the main mouthpiece of
our movement. The editors were R. Caniap and H. Reichenbach. The
first issue began with the paper, “The Turn in Philosophy," by
M. Schlick. I shall quote some lines in order to show that an opti-
mistic belief in the new trend was the keynote of this journal. Schlick
writes:

I am convinced that we are in the middle of an altogether final turn in
philosophy. I am justified, on good grounds, in regarding the sterile conflict
of systems as settled. Our time, so I claim, possesses already the methods by
which any conflict of this kind is rendered superfluous; what matters is only
to apply these methods resolutely.

In the same year (1930) Schlick published a paper, “Personal Ex-
perience, Cognition, Metaphysics,”” in which he writes:

All cognition of the being is achieved, in principle, by the methods of die
special sciences; every other kind of ontology is empty talk. Metaphysics is

” M. Schlick, “Erleben, Erkennen, Metaphysik," Kantstudien 31, 146 (1926).

modern science and its philosophy

impossible because its goals contradict one another. If the metaphysician
longs only for personal experience, his longing can be satisfied by poetry
and art— or by life itself. But if he longs for a personal experience of the
transcendent, he confuses life and cognition, he chases futile shadows.

For Schlick, as we know, “cognition” is the construction of a system of
symbols that denotes uniquely the world of facts. It is therefore funda-
mentally different from personal experience.

This strong optimistic feeling is psychologically the feeling of a
turn. You can ride in a car at high speed and you do not feel any-
thing so long as the velocity remains unchanged. But if a turn or an
acceleration takes place, you experience a strong reaction. Today, the
movement of logical positivism is no longer so conspicuous. It had
produced a turn in philosophy, which afterwards moved in a new
direction and rather smoothly. I quote a passage from a philosopher
who is by no means a follower of what is now called logical positivism.
C. West Churchman writes: “

Few can doubt the healthy impact that the positivist position has had
upon modes of inquiry; it has sharply distinguished the schools of thought,
and has raised a standard under which the proponents of experimental
methods can fight their battles against a reactionary movement. To return to
a prepositivistic viewpoint is to retiun to a prescientific viewpoint, to become
a reactionary as an advocate of the indisputable power of the sovereign in
the eyes of one with a democratic outlook.

We find a similar position even in the most recent book of F. S. C.
Northrop “ who, in some sense, attempts a justification of metaphysics.
He has been, however, in all his writing a very independent thinker
who has given much thought to the foundations of science and par-
ticularly to the interdependence between the philosophy of science
and die cultural background. He writes:

“In any event, the great merit of logical positivism and its main aim is
satisfied, even if one leaves the scientific concepts and their meaning just as

® C. W. Churchman, Theory of Experimental Inference (New York: Macmil-
lan, 1948).

*®F. S. C. Northrop, The Logic of the Sciences and the Humanities (New
York: Macmillan, 1947), pp. 113, 114.

historical background

one finds^them, as prescribed by the scientists in the postulates of some
specific deductively formulated theory. The important desideratum at which
the logical positivists were aiming, namely operational verification, can
nonetheless be obtained. There are many signs that contemporary logical
positivists have now come to this position.

As a matter of fact, if one traces the history of logical positivism, one
will see that this has been always the position of the “scientific world
conception.” This becomes clear if one considers Schlick’s position in
“Space and Time” (Sec. 13).

To estimate how sharp the turn was for which logical positivism
was responsible, we have to compare its position with the views of the
school of traditional philosophy that was the nearest to it in spirit and
in time. We choose for comparison H. Vaihinger’s “Philosophy of ‘As
If”’ (1911), a very ingenious and in its time very famous book, a typi-
cal example of what I called the disintegration of traditional philosophy
by neo-Kantianism. Vaihinger tries to show that the concept of an
atom (which he identifies with a mass point) in physics is a useful
"fiction” although it is logically self-contradictory. He says:

An entity without extension that is at the same time a substantial bearer
of forces— this is simply a combination of words with which no definite mean-
ing can be connected. “Simple atoms,” that must yet be something material,
cannot be causae verae, cannot be actual things. Since, however, the physi-
cist does require atoms for his construction, how is this contradiction to be
solved? How are we to rescue science from this dilemma? “

Vaihinger thinks that the method actually used in science is to

speak of atoms without really meaning to assume them . . . Unquestionably
this conceptual method is die most convenient one, but this constitutes, of
course, no proof of its objective-metaphysical validity."

Vaihinger’s view is a clear indication of the situation in philosophy
immediately before the rise of logical positivism. There was a com-

“Hans Vaihinger, Die PhUosophie der “Ah Ob" (1911); English translation
by C. K. Ogden (ed. 2, Bames and Noble, 1935), p. 219. Incidentally, in this
book the term “logical positivism” was used for the first time, although in a some-
what different sense from the one it now has.

»16id.,p. 222.

modern science and Its philosophy

plete lack of understanding that one must distinguish between a
structural system having exact logical coherence with the world of
facts, which are described with a certain vagueness, and the opera-
tional definitions, which connect both domains and participate in the
preciseness of the first and the vagueness of the second.

2 \» P. W. Bridgman's Theory of Meaning

About the same time when the “scientific world conception” group
were arranging their first public meeting, P. W. Bridgman published a
book ® in the United States in which he reacted to the same situa-
tion by which this group had been faced. In a broad sense, we can
characterize his work also as an attempt to integrate Mach, Poincare,
and Einstein into a coherent picture of modern science. Bridgman’s
field was not mathematics or symbolic logic but experimental physics.
He has been a man of the laboratory who preferred to do things
rather than set up a long chain of arguments. His approach is therefore
different from that of the Central European group. It was, in a way,
more similar to Mach’s, who was also essentially an experimentalist.
Bridgman found out what was the salient point in the integration of
Mach and Poincare. Reichenbach had explicitly pointed out that
what is needed is a bridge between the symbolic system of axioms and
the protocols of the laboratory. But the nature of this bridge had been
only vaguely described. Bridgman was the first who said precisely
that these “relations of coordination” consist in the description of
physical operations. He called them, therefore, “operational defini-
tions.” This name has been generally accepted. Bridgman was also
very definite in stating that a theory which does not contain the opera-
tional definitions of its abstract terms is meaningless. In this way he
arrived at a concept of “meaning” and “meaninglessness” that was
similar to the concept advanced by Carnap and his group.

Bridgman, however, formulated the criterion of meaning in a
much more concrete way. He did not restrict himself to the general
prescription of how to investigate the meaning of a statement but
investigated elaborately the operations that have to be carried out in
order to define the meaning of physical terms like “length” or “thermal

historical background

capacity.* By these investigations he found, for example, that the
operations by which one can distinguish between heat conduction
and heat radiation, or between heat supplied and mechanical work
supplied, cannot be performed in all cases. Only if the phenomena
investigated are of a simple type are these operations feasible. There-
fore, terms like “heat conduction” or “mechanical work” do not have
a meaning under all circumstances.

Bridgman has contributed much to the new philosophy which has
developed along with twentieth-century science. He has advocated
strongly the view that the domain of phenomena within which a word
has meaning is restricted, and no word has meaning if we do not in-
dicate the circumstances under which it is used. Bridgman has also
pointed out repeatedly that this new “semantic” aspect is bound to
have great repercussions upon discourse in politics and religion.”

In 1931 Carnap was appointed professor of natural philosophy at
the University of Prague. I succeeded in bringing about this appoint-
ment, despite the strong opposition of the adherents of traditional
philosophy, because of a happy coincidence. At that time the Faculty
of Arts and Sciences was divided into a Faculty of Humanities and a
Faculty of Science. All professors of philosophy were in the Faculty
of Humanities and the Faculty of Science gave no instruction in
philosophy. The president of the Czechoslovakian Republic, Thomas
G. Masaryk, who had himself been a professor of philosophy, believed
strongly in the educational value of philosophy. He insisted that the
Faculty of Science should have a philosopher of their own. I suggested
Carnap, and as there was no advocate of traditional philosophy left,
the science faculty agreed. From 1931 on we had in this way a new
center of “scientific world conception” at the University of Prague.

22. The Spreed of Logical Empiriciim

My own interest, which had been for a long time diverted from the
problems offered by the philosophy of science, returned now to the
object of my earlier years. The intellectual situation was now in a
certain respect a similar one. The new science of quantum theory gave
“ P. W. Bridgman, Yale Review 34, 444 (1945).

modern science and its philosophy

rise to a repetition of the crisis that had been precipitated about 1905
by the relativity theory, but with even greater intensity. Again it was
maintained that scientific method had failed. The new theories do not
even claim to give an “explanation” of the physical phenomena. They
claim only to offer mathematical formulas from which the observed
phenomena can be derived. The “explanation” is left as a field for
metaphysical theories, which would claim to give the “real causes” of
1 things. The argument went mostly that relativ ity as well a s quantum
J theory give mathematical patterns without any causal justification.

Remembering our old arguments in the Vienna coffeehouses
around 1907 about Abel Rey, Ernst Mach, and Henri Poincar6, I
devoted some work to applying the newly developed “scientific world
conception” to overcome the new crisis. I tried to show that there is
not the slightest reason to see in twentieth-century theory an argu-
ment for anjdealistic o r spiritualis tic world conception, and that this
opinion only arises from a lack of scientific formulation of the new
physical theories. This lack has its source in the poor training of
physicists in philosophy, which makes them often faithful believers in
the metaphysical creeds imbibed in their early youth “from a nurse or
a schoolmaster.” “ In Chapters 6 and 7 of the present book I at-
tempt to give an analysis of physical theories on die basis of the new
ideas; the scientific argument is carried through consistently without

suddenly breaking into vague metaphysical discourse. While these

chapters are more or less devoted to a
physics. Chapters 8 and 9 contain a !

Iphysics, Chapters 8 and 9 contain a special discussion of modem

q uantum the ory from the same viewpoint, including some remarks on
“d^erminism” that take up, in a new way, the problem of Chapter 1.

'if we look from another angle upon those misinterpretations of
physical theories, it is evident that they are not the result of some

intellectual inability. Their real source is the urge to find support for
a metaphysical creed that, for some reason, one cherishes. And this

reason is, as we have already hinted, the fitness of this metaphysical
creed to bolster up some political or religious creed that one believes

“A. N. Whitehead, The Principle of Relativity (Cambridge: The University
Press, 1922). ,

historical background

to be indispensable for the well-being of mankind. ^This sociological
aspect has been for many years familiar to me from the discussions of
our old Viennese group and, in particular, from the attention that I
later paid to the influence of religious and politica l creeds upon
scientific theories in two specific cases; Duhem’s presentation of the
taken by the Roman Church against the Copemican theoiy, and
Lenin’s attacks on Mach’s conception of physics. I have touched upon
this aspect in Chapter 5 and have devoted all of Chapter 10 to it. The
Copemican confl ict is treated in Chapter 13, the specific nature of
the Soviet philosophy (dialectical materialism) and, in particular, its
relation to positivism and empiricism are described in Chapter 11.

At the time of the meeting in Prague (1929) the Vienna Circle
and Reichenbach’s group in Berlin were a small number of dissident
people hemmed in by the vast ocean of German school philosophy,
which was more or less a development of Kantian metaphysics. It was
considered to be a specific "German philosophy’’— namely, “German
idealism’’— and philosophies of other types were regarded with a
certain suspicion as something "un-German” and “foreign.” The
workers for a "scientific world conception” had no hope of finding any
considerable encouragement in Germany. Neurath described this
cultural and historical situation in his small book, “The Development
of the Vienna Circle and the Future of Logical Empiricism.” “ Neurath
writes that the Kantian influence had been slight in the Universities of
Vienna and Prague and that their philosophy avoided the "Kantian
interlude” and passed directly from Leibniz to modern positivism. He
continues, "The influences of English and French thinkers are frequent
and things happen in Austria parallel to what happens in Warsaw,
Cambridge, or Paris, rather than to what takes place in Berlin.”

Although German science had developed along international lines
and no serious scientist would have objected to any foreign influence,
in philosophy things were different. There was a strong tendency to
overrate “German idealism” and to minimize British, French, and

"*0. Neurath, Le DSveloppement du Cercle de Vienne et Vaoenir de Vem-
pMsme logique, French translation by General Vouillemin (Paris: Hermann,
1935 ).

modern science and its philosophy

American philosophical trends. We felt very soon that th6 future of
the “scientific world conception” was to break through this wall and
to make contact with “foreign” philosophies. This feeling turned out
to be entirely correct and^e met friendly interest on the part of
American, British, and French thinkers. In the United States there
was a natural common ground, the work of the American pragmatists,
in particular of C. S. Peirce. Charles W. .Morris had cultivated es-
pecially the ties between pragmatism and the Central European
positivism. He coined for the result of the very close cooperation of
these groups the name “logical empiricism,” which seems to me to
denote the salient point better than any other name. E. Nagel (now
at Columbia) and W. V. Quine (now at Harvard) came to Vienna and
Prague, 'as Morris (now at the University of Chicago) had done, to
make personal contact with Schlick, Carnap, and the other workers in
this field.

^n Great Britain our natural link was L. Wittgenstein, whose own
education had been half Austrian and half British, and, through him,
Bertrand Russell. The brilliant young Oxford philosopher, A. J. Ayer,
also came to Vienn^ and published the most readable book on logical
empiricism that has been written in English, and perhaps the most
readable book altogether."

(in France, the advocates of the “new positivism” were naturally in-
terested in our movement. L. Rougier started his philosophic work on a
basis similar to that of Schlick) He took his start from Poincare, tried
to integrate Einstein into the “new positivism,” and wrote the best all-
round criticism of the school philosophy that I know of, "The paralo-
gisms of rationalism.” "

Marcel Boll, an able physicist himself, saw in the Viennese move-
ment a valuable contribution to a renewed and more vigorous positiv-
ism and a support of progressive thinking and acting. He translated
writings of Carnap, Reichenbach, Schlick, and myself into French.

We encountered also a strong interest in a group of French neo-

J. Ayer, Language, Truth, and Logic (London: Gollanc?:; New York:
Oxford University Press, 1936).

®®L. Rougier, Les paralogismes du rationcdisme (Paris: Alcan, 1920).

historical background

Thomists. great influence of the neo-Thomist, P. Duhem, upon the
Viennese group repeated itself now in reverse. The French general,
Vouillemin, recommended our group because we replaced the spelling
“Science” modestly by “science.” He also translated several papers of
the Vienna Circle into French and published a small book, “The Logic
of Science and the Vienna School,” ” in which he gave his interpreta-
tion of logical empiricism. The French neo-Thomists of this group saw
in logical positivism the destroyers of idealistic and materialistic meta-
physics, which they regarded as the most dangerous enemies of
Thomism.

To organize this international cooperation a preliminary conference
was held in 1934 in Prague, at which Charles Morris and L. Rougier
participated. The ground was laid for arranging international con-
gresses “for the unity of science,” which were to be held every year.
They actually met in 1935 in Paris, 1936 in Copenhagen, 1937 in
Prague, 1938 in Cambridge, England, and 1939 in Cambridge, Massa-
chusetts, at Harvard University.

23. Teaching fhe Philosophy of Science of Harvard

In the year 1936, just while the Congress for the Unity of Science
was in session at Copenhagen, Professor Schlick was assassinated near
his lecture hall in the University of Vienna by a student. At the court
trial the attorney for the defendant pleaded extenuating circumstances
because the student was indignant about Schlick’s “vicious philosophy.”
Everyone who knew Schlick had been full of admiration for his noble,
humane and restrained personality. The political implications of the
expression “vicious philosophy” were obvious. The student received
a ten-year prison term. When, however, two years later, the Nazi troops
occupied Vienna and arrested a great many people, Schlick’s murderer
was released from prison.

The shots directed at Schlick were a dramatic indication of the dis-
persal of the Central European positivism that was taking place under
the pressure of the advancing Nazi power. At the end of 1938 this

Le general C. E. Vouillemin, La Logique de la science et rdccle de Vienne
(Paris: Hermann, 1935).

modern science and its philosophy

process was completed. ^By far the greatest part of the Central
Europeans who had worked along the lines of logical positivism had
left their countries. The immediate reason was either to escape politi-
cal persecution, or, in many cases, just the feeling that under the
dictatorship of the Nazis there would be no place for a philosophy
guided by logic and experience. The majority of the emigrants have
lived since in the United States, a smaller part in Great Britain^

When I arrived in the United States in October 1938, I started a
lecture tour during which I spoke at twenty-odd universities and col-
leges on the philosophic interpretations of modem physics. Chapter 7
of this book presents one of these lectures.

Since the fall of 1939 I have had the privilege of teaching at
Harvard University not only mathematical physics but also the philoso-
phy of science. This teaching has been a great experience for me
and has been of great influence on my philosophical writing. I started
with an audience of about fifteen students. Since this was an unusual
subject I did not quite know what to tell them. I began by presenting
to them the logical structure of physical theories as envisaged by
logical empiricism. But very soon I noticed that this was not the
right thing to do. The frequent discussions that I had with the stu-
dents showed me what they really wanted to know. By a process of
interaction, a program was finally worked out that was a compromise
between what I wanted to tell the students and what they wanted
to know.

At that time Harvard University set up its “General Education
Program.” This was a great help to me since it was based on the
deficiencies of the traditional curriculum as felt by the students, the
faculty, and the general public. President J. B. Conant urged, in par-
ticular, a new approach to the teaching of science. He stressed that
science teaching has to be linked up with a presentation of the his-
torical, cultural and psychological background of the work done by
the great scientists. This program was later developed in Mr. Conant’s
book. On Understanding Science.^^

“J. B. Conant, On Understanding Science (New Haven: Yale University
Press, 1947).

historical background

Stimukted by all these factors and particularly by the rapidly in-
creasing interest of the students in the philosophical and cultural
implications of science (I had later an audience of more than two
hundred fifty), it became more and more clear to me how to work out
a program for my students. I now put the greatest emphasis on pre-
senting physics, and science in general, as part of our general pattern
of thinking and acting. I presented it on one hand as a logical system
that has to be checked by physical experiments and on the other hand
as one of the means of expressing man’s attitude towards the world,
the small world of society and politics and the large world that is our
astronomical universe. This more historical approach has been familiar
to me since my student years from the meetings with my older friends.

All my papers written after 1940 follow this line. Chapter 11 of
this book describes the interaction between the advance in science and
the changes in metaphysical systems. Its point is that a great many
metaphysical systems are merely abandoned systems of science. In
Chapter 12 the Copemican conflict is discussed from the same view-
point, particular stress being laid on the role that could be played by
the intervention of political powers. Chapters 14 and 15, which are
closely connected with each other, discuss directly the role that in-
struction in the philosophy of science is to play in the college cur-
riculum. By the time I came to write them, I had collected a great deal
of experiential material about this problem. My point was now that
the philosophy of science should, on one hand, give to the science
student a more profound understanding in his own field, and on the
other hand, be for all students a link between the sciences and the
hiunanities, thus filling a real gap in our educational system.

In all my writing before 1947 I had stressed the point that science
gives no support to metaphysical interpretations, of whatever type. I
had discussed these interpretations only as reflecting the social en-
vironment of the philosopher. However, after that time, as a result of
contact with my students and fellow teachers, I became more and
more interested in the question of the actual meaning of the meta-
physical interpretations of science— idealistic, materialistic, relativistic,
and others. For the fact that a great many scientists and philosophers

modern science and its philosophy

advance such interpretations and cherish them is as firmly established,
by our experience, as any fact of physics.

I now began a new series of investigations into the meaning of
metaphysics within the framework of logico-empirical and socio-
psychological analysis. The first preliminary result of these investiga-
tions is published in Chapter 16 of the present book.

In 1940 Professor Harlow Shapley, Director of the Harvard College
Observatory, introduced me into the Conference of Science, Phi-
losophy and Religion, which meets e%'ery year. This Conference is a
group of philosophers, educators, social workers, and ministers of all
denominations, and includes a sprinkling of scientists. They are in-
terested particularly in the contributions that each of these fields can
make to the understanding and supporting of the democratic way of
life. The leaders in this group have been, besides Dr. Shapley, Dr. Louis
Finkelstein, President of the Jewish Theological Seminary of America,
and Dr. Lyman Bryson, Director of the Educational Department of the
Columbia Broadcasting System. From these meetings 1 have learned
more about the attitudes of different groups of people toward science,
and what points in the philosophy of science support or are believed
to support a certain way of life. The large majority in these meetings
has been rather critical of the scientific outlook and its contribution
to human welfare.

I addressed this group several times between 1940 and 1947. My
contributions centered mostly around the question of whether the
“relativism” of modem science is actually harmful to the establishment
of objective values in human life. I made an argument to prove that
the “relativism of science” has also penetrated every argument about
human behavior. “Relativism” is not responsible for any deterioration
of human conduct. What one calls “relativism” is rather the attempt to
get rid of empty slogans and to formulate the goals of human life
sincerely and unambiguously. My contributions to these meetings will
be published “ in due time, under the title “Relativity— a richer truth.”

^ Beacon Press, Boston.

CHAPTER

experience and the law of causality

T he French mathematician Henri Foincar4, in two books ^ on the
philosophy of Science, “Science and Hypothesis,” and “The Value
of Science,” presented the point of view that many of the most
general principles of theoretical science— such as the law of inertia,
and the principle of conservation of energy—about which one often
wonders whether they are of empirical or a priori origin, are actually
neither of these, but purely conventional definitions depending on
human arbitrariness.

The purpose of the present paper is to extend this conception to
the principle that is in a certain sense the most general in all theoretical
science, the law of causality. The direct stimulus for this undertaking
was given by a book which, as a matter of fact, follows an opposite
tendency, the sagacious and in many respects unprejudiced work,
“Concepts and Principles of Natural Science,” by Hans Driesch.® The
author sets out to show that the principle of conservation of energy
has an a priori nucleus which is no other than the law of causality in
its precise formulation. In order to demonstrate the apriorily of the en-
ergy principle, Driesch presents a series of ingenious arguments which

Foincare, Science and Hypothesis (Science Press, New York, 1905;
original, 1902); The Value of Science (Science Press, New York, 1907; original,
1905).

Driesch, Naturbegr^e und NatururteUe (Leipzig, 1904).

modern science and its philosophy

show that experience can never disprove the principle in' question.
This array of arguments calls to mind in an astonishing way that used
by Poincare for his conception of the energy principle as a convention.
The agreement is all the more striking since evidently neither author
was influenced by the other. Although the conclusions reached are
quite different, the two arguments are very similar. Since that of
Driesch is to a large extent applicable to the law of causality, I have
found in it new support for my conception of this law, which I felt to
be a necessary consequence of the arguments presented in Poincare’s
papers.

The thesis that we shall try to prove states that the law of causality,
the foundation of every theoretical science, can be neither confirmed
nor disproved by experience; not, however, because it is a truth known
a priori, but because it is a purely conventional definition. VVe shall take
as a basis the form of the law of causality that is freest from undefined
and ambiguous expressions and contains only the essentials, referring
directly to the data of the senses.

The law states that if, in the course of time, a state A of the universe
is once followed by a state B, then whenever A occurs B will follow it.

This statement contains everything that is the real content of the
law of causality. It is important to understand that the law can be
applied only to the whole universe and not to a part of it. This, how-
ever, makes it impossible to test the law empirically. In tlie first place,
one can never know the state of the whole universe, and in the second
place, it is in general not certain whether it is possible for a state A
of the universe ever to return. If no state A could ever be repeated, the
law would be meaningless theoretically, since it refers only to recurring
states.

Fortunately, it is not the exact law of causality itself which finds
application in science, but a formulation of it that asserts only some-
thing approximate. This says that if, in a finite region of space, die
state A is at one time followed by the state B and at another time by
the state C, we can make the region sufficiently large by adding to it its
environment that the state C becomes as close to the state B as we
please.

experience and the law of causality

In otKer words, in finite systems the law of causality is the more ^
nearly valid the larger the system. In the application of the law to a
finite system, the answer to the question whether the system is large
enough depends on the degree of accuracy required for the occur-
rence of the predicted effect. This can be shown by a simple example
taken from astronomy, the science that has been worked out most
rationally. Let us consider the system consisting of the sun and the
earth. A state A of this system, defined by a particular distance of
separation and relative velocity of the two bodies, is always followed
by the same series of states, no matter how often A is repeated; but we
must not take the word “same” too exactly. For, in reality, the series of
states following A also depends on the distances and velocities of all
the other planets and the fixed stars as well, and we must include them
in the system. The more celestial bodies we include, the more ac-
curately is the law of causality obeyed. However, if we take into the
system only the planets with their satellites, the accuracy is sufficient
for all practical purposes. We see from this example that there do exist
finite systems to which the law of causality is applicable.

Whether a given system will behave in this way cannot be known
beforehand; for this reason the so-called inductive method has been
developed. When an investigator sees “that in a system the state B
follows the state A, not once but often, he will say that A is the cause
of B.” This means nothing else, however, than that the law of causality
is applicable to the system under discussion. For an all-embracing
system, a single case in which B follows A is enough to enable one to
draw conclusions for all times thereafter. For a finite system, however,
it is necessary to decide in every case whether the law of causality is
applicable. Naturally, such a decision can never be a final one, for the
law of causality as applied to finite systems is not the real one, but only
a substitute for it. The real law itself is only an ideal which the law for
finite systems approaches as a hmit as these systems are made larger
and larger. '

Here we do not wish to concern ourselves with the difficulties
arising from the finiteness of empirical systems. It will soon appear that
these are relatively unimportant in comparison with arguments that

modern science and its philosophy

would place the law of causality in a peculiar light even if it were
rigorously valid for finite systems, which will be assumed hereafter.
We have, then, a finite system for which the law is valid that if the
state A is followed once by the state B, then A will be followed every
time by B. In this statement there occurs, however, a single word—
“state”— that is not explainable directly through any reference to sense
data. And the analysis of this word will suffice to demolish this seem-
ingly so strongly built meaning of the law.

What is a “state of a system?” The most obvious explanation would
be that by state we mean the ensemble of the perceptible properties of
a system. This would be a clear meaning. However, if we take the
word "state” in this sense, the law of causality becomes incorrect, as
can be seen from simple examples. Let us assume that the system con-
sists of two iron rods, lying side by side on the table, that is, in state A.
Left to themselves, they will continue to lie quietly; that is, A is fol-
lowed by A. If now we replace one of the iron rods by a magnetized
one of exactly the same appearance, the initial state, according to our
definition of the word “state,” will be the same as before, namely, A.
The rods will now move toward each other, however; that is, A is now
followed, not by A, but by B. In order to be able to say that the law of
causality is still valid, we must say that the initial states were only ap-
parently the same. We must include in “state” not only the totality of
perceptible properties, but also another, namely, in our example,
magnetization. A property belonging to the definition of the state is
called a state variable of the system.

How does it come about that we assign to bodies imperceptible as
well as perceptible properties? Such properties— electric charge, chemi-
cal affinity, and so on— are characteristics that indicate how the body
possessing them behaves when brought into certain situations. They
are, according to Driesch, "the aggregates of possibilities, regarded
as reality.”

This, however, means only that if a body in a given situation be-
haves differently from another body the state of which, in the sense
first defined, is the same, we assign to it new state variables in addition
to the perceptible ones. This in turn means only that if the law of

experience and the law of causality

causality is not valid according to one definition of the state, we re-
define the state in such a way that the law is valid. If that is the case,
however, the law, which appeared to be stating a fact, is transformed
into a mere definition of the word “state." We can express the law in
the following form; “By the word ‘state’ one understands the per-
ceptible properties of a system of bodies, plus a series of fictitious
properties, of which so many are included that the same states are
always followed by the same states.” In this form the “law of causality”
no longer looks at all like a law.

Because of the fact that the word “state,” which occurred in that
form of the law of causality first taken as a basis, is only defined by
this law, the latter loses the character of a factual proposition and
becomes a definition. Of a definition, however, one cannot say that it
is empirical or a priori; it is only a product of human imagination. ,

The conclusion to which the foregoing refiections lead is that “the
law of causality is only the establishment of a terminology.” Because
this law forms the basis of the whole of theoretical science, the latter
itself is also nothing else than a suitably chosen terminology. Whereas
experimental science describes the properties of bodies as given by our
senses, and the changes in these properties, the task of theoretical
science is to provide bodies with fictitious properties the chief purpose
of which is to insure the validity of the law of causality. Theoretical
science is not research but a sort of remodeling of nature; it is work of
the imagination. From this it is clear whence the so-called pure— that is,
a priori— science, the possibility of which led Kant to write his Critique
of Pure Reason, derives its conviction of being right. The principles of
pure science, of which the foremost is the law of causality, are certain
because they are only disguised definitions.

Pure science states nothing about empirical nature; it only gives
directions for portraying nature. All the arguments which Driesch has
arrayed so ingeniously for the existence of a piure science show indeed
that there are principles independent of our experience, but fail to
explain why this is the case. The reasons are completely revealed by
the conception presented above.

i^Tbus we see that the latest philosophy of nature revives in a striking

modern science and its philosophy

way the basic idea of critical idealism, that experience only serves to
fill in a framework which man brings along with him as a part of his
nature. The difference is that the old philosophers considered this
framework a necessary outgrowth of human organization, whereas we
see in it a free creation of human imagination.

How often the question has been put: “How can it happen that
man can work out all of outer nature, which is, after all, completely
independent of his mind?” Are not nature and the human intellect in-
commensurable things? From our standpoint it is easy to answer that
the nature which the human mind rationalizes by means of theoretical
science is not at aU the nature that we know through our senses. The
law of causality and with it all of theoretical science have as their
object not empirical nature but the fictitious nature of which we spoke
above. The latter, however, is not only the object, but also the work
(and work, not in any metaphysical sense, but in the ordinary sense)
of man; hence it can of course be completely comprehended by him.

To the fundamental questions of theoretical science, experience and
experiment can never give an unequivocal answer. If I wish, I can
provide all bodies with state variables that are all qualitatively dif-
ferent, in order to fulfill the law of causality. I can regard heat, elec-
tricity, magnetism, as properties of bodies, essentially different from
one another, just as is done in modem energetics, and as Driesch does.
On the other hand, if I wish, I can get along without introducing quali-
tative differences. For example, I can introduce only the motion of
masses; but then, in order to obtain the necessary diversity, I must take
refuge in unconfirmable hidden motions. This leads to the purely me-
chanical picture of the world, which Democritus dimly conceived as
an ideal, and which occurs mostly in the form of atomism. This purely
quantitative picture of the universe, striving to manage with a mini-
mum number of qualities, was given its most logical development in
the book ‘Thilosophy of Inanimate Matter” by Adolf Stohr,® where
even the qualitative specificities still adhering to mechanical atomism
were suppressed in favor of purely geometrical-quantitative schemes.
This work, as the most radical carrying out of the program of the
* A. St&hr, Phttosophie der unbelebten Materie (Leipzig, 1907).

^ experience and the law of causality

atomists, occupies a significant place in the literature of natural
philosophy. In a quite different way, H. A, Lorentz and his pupils have
created a quantitative world picture by breaking away from the mech-
anistic tradition and introducing as state variables electric charge
and electric and magnetic field intensities. Thus arose the electro-
magnetic picture of the world. Among all these, it is not possible to
choose uniquely on the basis of experience. One may be simpler, an-
other more complicated, but none true or false.

We see that it is not at all a scientific question, in the narrower
sense, what world picture I make for myself. The world pictures are
only more or less different expressions used for the same thing—
empirical nature.

Furthermore, the same is true of a question which has long held
sway as a so-called question of world conception, the answer to which
is above all demanded of the scientist. It is a question that seems to
carry with it an i nfi nite number of emotional values, and yet it is only
a question of terminology. It is the question (to return at the end to
the book of Driesch mentioned at the beginning) whether the phe-
nomena of animal and plant life can be explained by means of the laws
of physics and chemistry, the question that is usually summarized in
the high-sounding expression, “vitalism or mechanism?”

We are indebted to Driesch for the first clear and unprejudiced
formulation of the problem which, following him, and with reference
to what has been said hitherto, we can express as follows: Must we, in
order to satisfy the law of causality in the domain of life, ascribe to
the body besides the properties (state variables) of physics and
chemistry, also other, qualitatively different properties? Driesch tries
to show that we must do this, and introduces entelechy, as a state
variable peculiar to living bodies. This attempt of Driesch’s to show
that it is impossible to get along with the state variables of physics and
chemistry alone seems to me not entirely convincing. To be sure,
Driesch shows that we can assume for the living processes a specific
state variable, but not that we must. For it is not possible to foresee
every trick that one might invent in the fiction of hidden combinations
of inorganic state variables. In favor of vitalism^ I should like to remark

modern science and its philosophy

that, just as I cannot force someone who regards heat as a specific state
variable to consider it as a motion of mass particles, so 1 cannot force
the adherents of entelechy to replace it by fictitious state variables.
However, that is not very important for the purpose of the present
work. What is important is that, from the bio-theoretical works of
Driesch, if we examine them from the standpoint adopted by us, it is
clear that the question “vitalism or mechanism?” is not a question of
fact. It is not a question to which a crucial experiment can answer yes
or no. It is rather a question the solution of which depends on the in-
genuity of the human imagination and can never be convincing to all
men. The question is not: “Is that thus or so?” It is rather: “Can we
paint the picture in this or in that style, or in both?”

With the question of world conception in the ethical-religious sense,
all this has nothing whatsoever to do.

CHAPTER

the importance for our times of Ernst Mach’s
philosophy of science

T hebe is something remarkable about the teachings of Mach.
Philosophers often ridicule or disdainfully reject them as the
work of a physicist dabbling in philosophy; physicists often
deplore them as aberrations from the right path of respectable, realistic
natural science. Yet neither physicists and philosophers, nor historians
and sociologists, nor many others, can get rid of Mach. Some attack
him passionately; others extol him with fervor. There is something
fascinating about his simple, straightforward teachings. In spite of
their simplicity they are stimulating and provocative. There are in-
deed but few thinkers who can provoke such sharp differences of
opinion, who are so inspiring to some and so utterly repugnant to
others. What is there in these doctrines that makes it impossible for
anyone, whatever his views may be, to avoid adopting some definite
attitude towards them?

This is what I should like to discuss in the present paper. I have
formed a fairly definite opinion about the position that Mach occupies
in the intellectual life of our times, and this position, I believe, will ex-
plain why the battle rages about him so furiously. It is not a question
here of the details of Mach’s teaching, often individually and his-
torically conditioned, but rather of their nucleus, which is just the
focus of the struggle. I will not speak therefore about the general at-

modern science and its philosophy

titude of Mach towards the psychophysical problem, nor about his
separate contributions to physics and psychology, but only about his
conception of the tasks and possible aims of exact science.

In recent years, among creatively active physicists and mathema-
ticians, there has become noticeable a reaction against the conceptions
of Mach. When one of the most outstanding theoretical physicists of
our time. Max Planck,^ and one of the foremost living geometricians,
E. Study," characterize these conceptions as being partly misleading,
partly incapable of being carried out, and partly actually harmful for
science, the fact provides food for thought and cannot be lightly
brushed aside.

What an investigator with the markedly constructive talents of
Planck dislikes above all in the views of Mach is his judgment of values.
•. For the investigator, every new theory that is supported by experiment
is a piece of newly discovered reality. According to Mach, on the other
hand, physics is nothing but a collection of statements about the con-
nections among sense perceptions, and theories are nothing but eco-
nomical means of expression for summarizing these connections. He
says:

' The aim of natural science is to obtain connections among phenomena.
Theories, however, are like withered leaves, which drop off after having
enabled the organism of science to breathe for a time.”

This phenomenalistic conception, as it is called, was familiar to
Goethe. In his posthumous “Maxims and Reflections” he says:

Hypotheses are the scaffolds which are erected in front of a building and
removed when the building is completed. They are indispensable to the
worker; but he must not mistake the scaffolding for the building.

And still more drastically:

^ M. Planck, Die Einheit des physikalischen Weltbildes (Leipzig, 1909).

”E. Study, Die realistische Weltansicht und die Lehre vom Raume (Bruns-
wick, 1914).

” E. Mach, Die Qeschichte und die Wurzel des Satzes von der Erhaltung der
Arbeit, written in 1871. An English translation, History and Root of the Principle
of the Conservation of Energy, was published in 1911.

Ernst Mach's philosophy of science

constancy of phenomena alone is important; what we think about
them is quite immaterial.

It will be said, however, that Goethe was not really a good physicist,
and that we can see in his case an example of how such basic prin-
ciples hinder the spirit of research. Thus Planck says;

When the great masters of exact investigation of nature gave their ideas
to science, when Nicholas Copernicus removed the earth from the center
of the universe, when Johannes Kepler formulated the laws named after
him, when Isaac Newton discovered gravitation . . . —the series could be
long continued— surely, economical points of view were the very last thing
to steel these men in their struggle against traditional opinions and dominat-
ing authorities. No, it was their unshakable belief— whether resting on an
artistic, or on a religious basis— in the reality of their world picture. In view
of these certainly incontestable facts, one cannot reject the surmise that, if
the Mach principle of economy were really to be put at the center of the
theory of knowledge, the trains of thought of such leading spirits would be
disturbed, the flight of their imagination crippled, and consequently the
progress of science perhaps fatefully hindered.*

That these fears in such generality are groundless can be readily
seen if one recalls the views of one of the greatest theoretical physicists
of the nineteenth century, James Clerk Maxwell, on the nature of
physical theories. One need only read the introduction to his essay on
Faraday’s lines of force (1855) ® to be convinced that he was com-
pletely an adherent of the phenomenahstic standpoint. Yet one cannot
say of him that such adherence in any way crippled the flight of his
imagination; indeed, quite the opposite. The conception of the rela-
tive worthlessness of the theory in comparison to the phenomenon
gives to the theorizing of such an investigator something especially free
and imaginative.

I am willing to concede that the phenomenalistic doctrine is
pleasing to those whose work in physics is descriptive rather than con-
structive. Many such people, who are capable of describing very neady

* Planck, op. cit., p. 36.

° Published in Cambridge Philosophical Society Transactions, 1864, and in
The Scientific Papers of James Clerk Maxwell, ed. by W. D. Niven (Cambridge:
The University Press, 1890), vol. 1.

modern science and its philosophy

definite— even if very special— phenomena, may regard themselves be-
cause of this doctrine as being sublimely superior to the imaginative,
creative spirit, whose works, after all, are only phantoms and
“withered leaves.” I do not believe, however, that for these people the
philosophy of Mach has crippled the imagination. Rather, it is the case
of an imagination crippled by nature, which uses the teachings of Mach
as a beautiful cloak to cover its deformity. It may have been cases like
these which cause Planck, at the end of the lecture cited above, to
hurl at the preachers of the phenomenalistic doctrines the Biblical
words: “By Aeir fruits ye shall know them.”

Concerning this criterion of the fruits I shall have more to say.
First, in connection with the same Biblical allusion, I should like to
introduce a quotation from Pierre Duhem about the value of physical
theories. Duhem was the most outstanding representative in France
of ideas similar to those of Mach. He said:

By the fruit one judges the tree; the tree of science grows exceedingly
.slowly; centuries elapse before one can pluck the ripe fruits; even today it is
hardly possible for us to shell and appraise the kernel of the teachings that
blossomed in the seventeenth century. He who sows cannot therefore judge
the worth of the corn. He must have faith in the fruitfulness of the seed in
order that he may follow untiringly his chosen furrow when he casts his ideas
to the four winds of heaven.”

These remarks of the greatest and most accurate student of the his-
tory of physics are perhaps the best answer to the opinion expressed
by Planck

that even our present world picture, although it shows the most varied colors
according to the individuality of the investigator, nevertheless possesses
certain features that can never be obliterated by any revolution, either in
nature or in the human mind.^

These enduring features arise, according to Mach, from the fact
that all possible theories must give the same connection between phe-

•P. Duhem, L’&oolution de la micanique (Paris, 1903), translated into Ger-
man by Ph. Frank and E. Stiasny as Die Wandlungen der Mechanik (Leipzig,
1912).

^ Op. ctt., p. 35.

Ernst Mach's philosophy of science

nomena; this very fact guarantees a certain constancy. The known
connections among phenomena form a network; the theory seeks to
pass a continuous surface through the knots and threads of the net.
Naturally, the smaller the meshes, the more closely is the surface fixed
by the net. Hence, as our experience progresses the surface is per-
mitted less and less play, without ever being unequivocally determined
by the net.

Since, according to Planck and Study, the basic principles of Mach
would do nothing but harm to physics, it is fortunate for physics that
these principles have never been thoroughly applied by their adherents,
even if it is a gloomy sign for the principles themselves. Thus Study
says about positivism, as he calls the doctrines of Mach:

We regard this principle as a perfect utopianism. The possibility of its
existence is based entirely on the fact that it is disavowed by its own fol-
lowers at every step. Up to now there has never been any serious attempt
to apply it consistently . . . We are dealing here with a question of prin-
ciple and must therefore distinguish between the theory of positivism and
the practice of the (fortunately for themselves) thoroughly inconsistent
positivists.®

Planck says similarly:

We then attain a more realistic mode of expression . . . which is actually
the one always used by physicists when they speak in the language of
their science.®

With biting sarcasm. Study says;

In numerous cases the hypotheses that are basely denounced at the
official reception (why not atomistics, too?) are admitted, under a different
name and through a back door especially arranged for this, into the sanctuary
of science. Such names and corresponding motivations are by no means few.
Without any effort the writer collected a full dozen of them: “most com-
plete and simplest description” (Kirchhoff) . . . “subjective means of re-
search,” “requirement of conceivabiKty of facts,” “restriction of possibilities,”
“restriction of expectation,” “result of analytic investigation,” “economy of
thought,” “biological advantage” (all of these employed by E. Mach).“

® Study, op. cU., pp. 36, 41.

® Quoted by Study, p. 37.

“Ibid., p. 37.

modern science and its philosophy

With equal mockery, Planck remarks:

I should not be at all surprised if a member of the Mach school were to
come out some day with the great discovery, that . . . the reality of atoms
is just what is required by scientific economy

Other authors, too, point out the glaring contradiction that exists
among the admirers of Mach between theory and practice. A peculiar
theory of the nature of physical theories is set up, but as soon as physics
really begins the positivist behaves practically like any other physicist.
A follower of Mach can proclaim that physics has to do only with re-
lations among sense perceptions, but the preacher of this doctrine
speaks as a physicist exactly like any one else, about matter and energy,
and even about atoms and electrons.

However, it is just this apparently so palpable contradiction that
can lead to the understanding of the permanent nucleus of Mach’s
teachings. Let us listen once more to Study:

The whole situation is a striking reminder of Kronecker’s proposal to
abohsh the irrational numbers and to reduce mathematics to statements
about integers; in this case, too, the suggestion has remained programmatic,
and for the same good reasons.*^

The analogy, as I see it, is a very appropriate one. But I should like to
give it a different interpretation from that of Study. It is obviously
pointless actually to express all theorems of mathematics as theorems
about integers. In principle, however, it is highly enlightening to know
that all theorems about irrational numbers, and hence also all theorems
about limiting values, could be expressed as theorems about integers.
Once this possibility has been substantiated, the whole of analysis can
proceed to develop as usual. But now when a theorem about deriva-
tives is set up and somebody begins to subtilize about it, asking
whether this theorem is really in agreement with the “nature” of the
differential and going into profound and skeptical deliberations con-
cerning this “nature,” he can be told quite simply: “I could express this

“ M. Flanck, “Zur Machschen Theorie der physikalischen Erkenntnis," Vtertel-
jahTsschrift fiir wisaenschaftliche Philosophie und Soziologie 34, 497 (1911).

“ Study, op. dt., p. 39,

Ernst Mach's philosophy of science

theorem, if I took enough time, as a theorem about integers; the nature
of this theorem is hence no more and no less mysterious than that of
the natural numbers.”

The situation is quite similar with respect to Mach’s physical theory
of knowledge. It is not a question of actually expressing all physical
statements as statements about relations among sense perceptions. It
is important, however, to establish the principle that only those state-
ments have a real meaning that could in principle be expressed as state-
ments about the relations among our perceptions. To express the law
of conservation of energy or the law of equipartition of energy among
all the degrees of freedom as statements about relations among per-
ceptions is just as laborious, but also just as superfluous, as to express
the theorem that the derivative of the sine is the cosine as a statement
about integers. In principle, however, both are certainly possible.

For the inner working of physics it is in most cases practically im-
material whether one has adopted Mach’s standpoint or not. Similarly,
in Kronecker’s lectures on integral calculus there is nothing to be found
that differs essentially from the presentation of other mathematicians.

Wherein, then, lies the value of the doctrines of Mach for physics?

My view is that their main value is not that they help the physicist
to go forward in his physical work, but rather that they provide the
means for defending the edifice of physics against attacks from outside.

One who examines dispassionately the concepts that today are at
the basis of the system of hypotheses of physics will hardly be able to
assert seriously that the atom, the electron, and the quantum form
really satisfactory ultimate building blocks. Every thinker who is some-
what inclined toward logical thoroughness can find many obscurities
in these concepts. Into these nebulosities boring doubt can penetrate
and try to shake the whole system of physics as the foundation of our
scientific world picture. Here Mach steps in and says:

All these concepts are only auxiliary concepts. What is significant is ffie
connection among phenomena. Atoms, electrons, and quanta are only links
to represent a connected system of science; they make it possible to derive
logically tlie immeasurable system of connected phenomena from a few
abstract principles. But these abstract principles are then only the means

modern science and its philosophy

to an economical representation. They are not the epistemological basis. The
reality of physics can never be shaken by any criticism of the auxiliary
concepts.

The work of Mach is therefore not essentially destructive, as it is often
represented to be; positivism is not, as Study calls it, a “negativism,”
but on the contrary is an attempt to create an unassailable position for
physics. As a matter of fact, Planck, too, recognizes this when he says:

To it [the positivism of Mach] belongs in full measure the credit for
having found again, in the face of tlireatening skepticism, the only legitimate
starting point of all investigation of nature, the sense perceptions.'^

That Planck condemns so sharply the conception of Mach seems to
me therefore to arise from the fact that he considers it only from the
viewpoint of its application within physics. It must be said, however,
that, even when regarded from this standpoint, the phenomenalistic
conception has already accomplished something and is perhaps capable
of accomplishing still more. In the boundary regions of physics, where
general concepts like space, time, and motion play a role, the epistemo-
logical position one takes is no longer entirely immaterial. Indeed, it is
universally known today that Einstein’s general theory of relativity
and gravitation grew immediately out of the positivistic doctrine of
space and motion, as Einstein himself has discussed in detail in his
reference to Mach.“

On the whole, however, I will gladly concede to Planck and Study
that positivism itself has not done much in clearing up individual ques-
tions of physics. But from this it does not follow that positivism is, in
general, of no value. The "fruits” of Mach’s teachings are indeed not
purely physical in character. It will be recalled that in recent years an
attempt was made to take advantage of the criticism of the basic physi-
cal concepts in order to proclaim the bankruptcy of the scientific world
picture. Bearing this in mind, one must ascribe a high value to the effort
of Mach to make physics independent of every metaphysical opinion.

H. Poincar^ says:

“ Planck, Die Einheit des phtjsikaliechen Weltbildes, p. 34.

“A. Eimtein, Physikailische Zeitschrift 17, 101 (1916).

Ernst Mach's philosophy of science

At first glance it appears to us that theories last only a day and that
mins heap up on ruins ... If we examine the matter more closely, how-
ever, we find that what decays is those theories which claim to teach us
what things are. But there is something in them which endures. If one of
them has revealed to us a tme relation, this relation has been acquired for
all time. We shall find it again under a new cloak in the other theories
which will reign successively in its place.'®

In a very determined manner, the French philosopher Abel Rey
emphasizes the importance for the general intellectual life of preserving
the edifice of physical ideas. He says:

If those sciences which, historically, have had an essentially emancipating
effect go down in a crisis that leaves them only with the significance of tech-
nically useful collections but robs them of every value in connection with
the cognition of nature, this must bring about a complete revolution in the
logical art and in the history of ideas . . . The emancipation of the mind,
as it has been conceived since Descartes, thanks to physics, is a most fatally
erroneous idea. One must introduce another way, and restore to a subjective
intuition, to a mystical sense of reality— in short, to the mystery — everything
that we believed had been taken away from it . . . If, on the contrary, it
turns out that there is no justification for regarding this crisis as necessary
and incurable . . . then the rational and positive method remains the best
nurse of the human spirit.'®

Here we have a very clear exposition of the dangers that would
arise for the whole world conception from a physics that had no other
epistemologic foundations than those auxiliary concepts which are so
much exposed to criticism.

Mach himself saw the real value of his theories in the fact that they
permitted setting up a connection, as free from contradictions as pos-
sible, between physics on the one hand and physiology and psychology
on the other. He who still doubts this has only to read the general sec-
tions of the Analysis of Sensations.^'' Here it is stressed again and again
that one must exert oneself to develop physics while using concepts

'® H. Poincare, La Valeur de la science (Paris, 1905); English translation by
G. B. Halsted, The Value of Science (New York, 1907).

'* A. Rey, La ThSorie de la physique chez les physiciens contemporains (Paris,
1907), p. 19.

" The Analysis of Sensations and the Relation of the Physical to the Psychical,
translated by C. M. Williams and Sydney Waterlow (Dhicago, 1914).

modern science and its philosophy

that will not have to be given up in a transition to a neighboring branch
of science.

From this effort of Mach to employ only concepts that will not lose
their usefulness outside of physics we can understand his opposition to
atomistics, which in particular has caused many physicists to turn
against him, It is true that atomistics, when applied to physiologic and
psychologic problems, easily leads into a blind alley. Such questions
arise as: “How can a brain atom think?” “How can an atom perceive
green, since, after all, it is itself only a miniature picture of a macro-
scopic body composed of perceptions?”

I will not deny that Mach allowed himself to be misled by this
argument into attacking the use of atomistics in physics more sharply
than can be justified. After all, the usefulness of the atomic theories in
this limited realm is certainly indisputable. His followers, as is gen-
erally the case, often saw in this weakness of the master his greatest
strength, and wished to banish the atom entirely from physics. I believe
that one can completely free the nucleus of Mach s teachings from this
historically and individually conditioned aversion to atomistics. The
■ atoms are auxiliary concepts just like others that can be employed
advantageously in a limited domain. They are not suitable for an
epistemological foundation. Once we have adopted this point of view,
we are all the freer in employing the concept of atoms wherever it is
admissible. I believe that even Planck would not object so much to the
kernel shelled in this way. It is then no longer so very strange when
one declares the atoms, if not their reality, to be a requirement of
economy. They can be the simplest means of representing physical
laws without thereby being suitable to form an epistemological founda-
tion.

In general, phenomenalism will neither particularly further nor
hinder the physicist in his field of work. Thus Maxwell, who doubtless
thought positivistically, wrote the work that laid the foundation for
the molecular theory of gases. The phenomenalistic conception be-
comes a danger only in those cases in which the requirement of
economy is not realized with equal intensity. The most noteworthy
historical example is perhaps Goethe’s doctrine of colors. However, if

Ernst Mach's philosophy of science

one wishes to pass judgment on a person of such strong individuality
one must not forget, as A. Stohr quite correctly points out, that the
requirement of economy may mean something quite different for
every individual.^ For one, it signifies a minimum of hypotheses; for
another, say, a minimum of different kinds of energy. The former is
the case for the extreme phenomenalist Goethe; the latter for the pure
mechanist.

It will perhaps be instructive, as a comparative case, to recall a
theoretical physicist who, as an immediate student of Mach, really tried
to construct a system of physics and chemistry in which no hypothetical
corpuscles, whether atoms or electrons, occur, and which embraces all
the phenomena known at present. It cannot be denied that Gustav
Jaumann in his numerous works has undertaken this task with great
constructive force.^“ I do not believe, however, that the result has
turned out to be really in the spirit of Mach’s teachings. To be sure, it
corresponds to the surface requirement that all atomistics be omitted,
but it hardly corresponds to the requirement of economy. A large num-
ber of constants are employed about which the theory can make no
prediction. The Jaumann system makes it possible only in a very
limited degree to derive phenomena, also with regard to numerical
values, from a small number of hypotheses. To show the independence
of physical research and the epistemologic basis, one can mention that
the most energetic attempt to refute the corpuscular theory of elec-
tricity, that of F. Ehrenhaft, has no connection whatsoever with
philosophic dogmas of any kind.

I believe that I have now made clear to some extent the significance
of Mach. In order fully to survey his position in the intellectual life of
our times, however, we must find a more remote standpoint, in order
to obtain a better view.

If we read the most important work of Mach, his Mechanics,^ we

A. Stohr, PhUosophie der unbelebten Materie (Leipzig, 1907), pp. 16 ff.

“ G. Jaumann, "Geschlossenes System physikalischer und chemischer DiSeien-
tialgesetze,” Sltzungsberichte der Wiener Akademie der Wissenschaften, math.-
scientific class, section Ila (1911), and many other papers in the same journal.

E. Mach, Die Mechanik in Hirer Entwickelung, historisch-kritisch dargestellt
(Leipzig, 1883); The Science of Mechanics; a Criticfl and Historical Exposition

modern science and its philosophy

that will not have to be given up in a transition to a neighboring branch
of science.

From this efiEort of Mach to employ only concepts that will not lose
their usefulness outside of physics we can understand his opposition to
atomistics, which in particular has caused many physicists to turn
against him, It is true that atomistics, when applied to physiologic and
psychologic problems, easily leads into a blind alley. Such questions
arise as: “How can a brain atom think?” “How can an atom perceive
green, since, after all, it is itself only a miniature picture of a macro-
scopic body composed of perceptions?”

I will not deny that Mach allowed himself to be misled by this
argument into attacking the use of atomistics in physics more sharply
than can be justified. After all, the usefulness of the atomic theories in
this limited realm is certainly indisputable. His followers, as is gen-
erally the case, often saw in this weakness of the master his greatest
strength, and wished to banish the atom entirely from physics. I believe
that one can completely free the nucleus of Mach’s teachings from this
historically and individually conditioned aversion to atomistics. The
atoms are auxiliary concepts just like others that can be employed
advantageously in a limited domain. They are not suitable for an
epistemological foundation. Once we have adopted this point of view,
we are all the freer in employing the concept of atoms wherever it is
admissible. I believe that even Planck would not object so much to the
kernel shelled in this way. It is then no longer so very strange when
one declares the atoms, if not their reality, to be a requirement of
economy. They can be the simplest means of representing physical
laws without thereby being suitable to form an epistemological founda-
tion.

Ernst Mach's philosophy of science

one wishes to pass judgment on a person of such strong individuality
one must not forget, as A. Stohr quite correetly points out, that the
requirement of economy may mean something quite different for
every individual.” For one, it signifies a minimum of hypotheses; for
another, say, a minimum of different kinds of energy. The former is
the case for the extreme phenomenalist Goethe; the latter for the pure
mechanist.

If we read the most important work of Mach, his Mechanics,^ we

A. Stohr, PhUosophie der unbelebten Materie (Leipzig, 1907), pp. 16 ff.

“ G. Jaumann, "Geschlossenes System physikalischer und cliemischer DiSeren-
tialgesetze,” Sltzungsberichte der Wiener Akademie der Wissenschaften, math.-
scientific class, section Ila (1911), and many other papers in the same journal.

“ E. Mach, Die Mechanik in ihrer Entwickelung, historisch-kritisch dargesteUt
(Leipzig, 1883); The Science of Mechanics; a Critical and Historical Exposition

modern science and its philosophy

shall find that in no section does he give us so deep an insight into his
innermost thoughts and intellectual inclinations as in the wonderful
chapter on theological, animistic, and mystical points of view in
mechanics. A wind of refreshing coolness blows from these statements.
What other authors have treated with vehement blustering, often with
a quiet announcement of a small auto-da-fe for the opponent, we see
here discussed in a genuinely scientific spirit. Yet throughout the
whole chapter there quivers an undertone of suppressed excitement.
One encounters there that state of being drunk with soberness which
has been attributed to the Age of Enlightenment. Indeed, Mach descries
in this age his spiritual home. In the chapter referred to, he says:

For the first time, in the literature of the eighteenth century enlightenment
appears to be gaining a broader base. Humanistic, philosophical, historical,
and natural science come into contact at this time and encourage one an-
other to freer thought. Everybody who has experienced this upsoaring and
emancipation, even if only in part, through the literature, will feel a life-
long melancholy nostalgia for the eighteenth century.

The personal acquaintances of Mach are aware that he was an
ardent admirer and reader of Voltaire. One of his former assistants.
Professor George Pick, informed me that Mach most emphatically con-
demned Lessing’s attacks on Voltaire. It is known, too, that Josef
Popper, of whom Mach says that for a long time he was the only man
with whom he could talk of his physical and epistemologic opinions
without precipitating a conflict, wrote a whole book devoted to the
defense, indeed the glorification, of Voltaire.

In my opinion, Mach was led in this predilection by a correct
estimate of himself. We can understand the role which as philosopher
he plays in the intellectual life of the present if we look upon his
teachings as the philosophy of enlightenment appropriate to our time.

Since this conception may easily be misunderstood, I must discuss
it more fully. First of all, the word “enlightenment” has acquired such
a bad connotation that perhaps many will see in this description a dis-
paragement of Mach. We must therefore try to make clear something

of its Principles, translated from the second German edition by Thomas J. McCor-
mack (Chicago, 1893).

Ernst Mach's philosophy of science

about the nature of this enlightenment and the reasons for its sub-
sequent neglect.

The first period of enlightenment in modem times began with
the downfall of the Ptolemaic world system. Copernicus tried to repre-
sent his system with the help of the concepts of the Aristotelian
scholastic philosophy. If, however, we read the dialogues of Galileo
about the two world systems, we encounter a very different tone.
Here the basic concepts of Aristotelian physics were taken up and
examined. In the teachings of Aristotle and his school, concepts like
“light” and “heavy,” “above” and “below,” “natural” and “forced”
motion, which were usable only for a very limited domain of experi-
ences, were made the basis of all theoretical physics. Galileo showed
that it was just this use of concepts outside of their natural realm of
validity that prevented the followers of Aristotle from understanding
modern physics. I do not mean by this to belittle Aristotelian physics,
which was an outstanding contribution for its time; I only wish to
show that what was enlightening in Galileo’s writings was his setting a
limit to the misuse of auxiliary concepts. And it is this protest against
the misuse of merely auxiliary concepts in general philosophical proofs ^
that I consider to be an essential characteristic of enlightenment.

Every period of physics has its auxiliary concepts, and every suc-
ceeding period misuses them. Hence in every period a new enlighten-
ment is required in order to abolish this misuse. When Sir Isaac Newton
and his contemporaries made the concepts of absolute space and time
the basis of mechanics, they were able to represent a large domain of
physics properly and without contradictions. It does not follow, how-
ever, that these concepts form a basis of mechanics that is satisfactory
from the standpoint of the theory of knowledge. When Mach criticized
the foundations of Newtonian mechanics and tried to eliminate absolute
space from it, he was the direct continuer of the work of Galileo. For in
absolute space we still had a remnant of Aristotelian physics. And
when Einstein joined Mach and in his general theory of relativity really
erected an edifice of mechanics in which space and time properly
speaking no longer occurred, but only the coincidence of phenomena,
the elimination demanded by Mach of the au^ary concepts of space

modem science and its philosophy

and time— useful only in a limited domain— was completed. Einstem is
the first tliinker to found a physics entirely free of Aristotelianism_,

In the Age of Enlightenment proper I also see a struggle against the
misuse of auxiliary concepts. If we leave out of the discussion the
political and social aspects, then, theoretically considered, the criticism
at that time was directed against the fact that theologic concepts,
which were formed for dealing with certain psychic experiences of
human beings, were made the foundation of all science throughout the
Middle Ages and even at the beginning of the modern era. These con-
cepts, no matter how appropriate they may be to restore hope and faith
to the struggling human soul, are nevertheless only auxiliary concepts
limited to this domain and are not suitable to be the epistemologic
foundation of our knowledge of nature. This critical point of view
emerged with great energy at that time. Today even theologians have
adopted the view that the Bible is not a scientific textbook. Indeed,
many Protestant theologians, proceeding still further in the direction
of enlightenment, now teach that all theologic truths are only state-
ments about inner experiences.

The natural science of the Enlightenment also needed au,xiliary
concepts for its development. In this way the concepts of matter and
atom began to play a decisive role. All at once these auxiliary concepts ,
were being applied to everything in the world; materialism, as it is
called, was bom. The fact that matter, too, was only an auxiliary con-
cept was forgotten, and people began to regard it as the essence of the '
world. Soon criticism of this viCxv set in. But although this criticism of
the misuse of auxiliary concepts usually serves only scientific progress,
here it had an additional effect. Since the ideas of the Age of Enlighten-
ment were not pleasing to the mling powers, the criticism of the misuse
of enlightenment was used to discredit enlightenment itself. Because
the rationalists misused auxiliary concepts, it was said of them that their
protest against the theologic world picture was unjustified. This view is,
of course, logically not tenable, for the fact is that their criticism did not
go far enough. However, there are always thinkers who are so con-
stituted that their thinking ultimately leads to the conclusions required
by the mling powers. An attempt was made to overthrow enlighten-

Ernst Mach's philosophy of science

ment by skepticism. Very appropriately Nietzsche says, of the part
taken in this work by certain philosophers:

The philosopher against his rival, e.g., science: now he becomes a
skeptic; now he reserves for himself a form of cognition which he denies to
the scientist; now he goes hand in hand with the priest so as not to arouse
the suspicion of atheism, materialism; he regards an attack on himself as
an attack on morality, virtue, religion, order— he knows how to discredit his
opponent as a "seducer” and an “underminer”; now he goes hand in hand
with the authorities.®^

In reality, however, only that part of enlightenment was refuted
which was not enlightenment. Nevertheless, because of the weight of
the authority of those involved, this disparagement of the great
achievements of the eighteenth century has had considerable influence.
There is perhaps no one among us who did not acquire a prejudice
against enlightenment at school dining his youth.

I admit, of course, that the great spirits of the Enlightenment,
Voltaire, d’Alembert, and the rest, were imitated by many shallow
writers who diluted their criticism more and more and descended to
intolerable banality, ending up by continuing themselves the misuse
of the auxiliary concepts. I admit, too, that this shallowness belongs
to the essence of the Enlightenment. Once the misuse of the old con-
cepts has been exposed, there is not much of an original nature left to
say. The temptation to dull triviality is strong and the number of those
who have fallen victim to it is great.

Nevertheless, all this provides no evidence whatsoever against the
philosophy of enlightenment. A man who has freed himself once and
for all from the fears of the usual stigma of heresy will say that the
task of our age is not to fight against the enlightenment of the eight-
eenth century but rather to continue its work. Since that time there
has occurred so much exaggerated application of entirely new auxiliary
concepts which are useful in hmited domains that there is plenty of
new work to be done.

To this work Mach dedicated himself. He approved enthusiastically
of the eighteenth-century enhghtenment. This does not mean, how-

Friedrich Nietzsche, The WiK to Fotoer, No. 248.

modern science and its philosophy

ever, that he began to idolize the eighteenth-century concepts like
materialism. Rather, in him lived the spirit of those great men; it drove
him on to protest against the misused concepts of his time just as they
had fought those of their time. Among the concepts that he fought
there happened to be many of the favorite concepts of eighteenth-
century enlightenment.

This is what I mean when I call Mach the representative of the
philosophy of enlightenment of our period. Since his youth was lived
during the time of materialism, it is no wonder that so many of his
works are devoted to the struggle against mechanistic physics and
atomistics.

If we accept Mach’s attitude as that of an enlightenment phi-
losopher it will be easier for us to understand many features of his
teachings and many of their effects. In the first place, there is their
strongly suggestive influence— one might even say their virulence—
which, in spite of many contemptuous judgments by professional phi-
losophers, commands attention. Study calls the positivism of Mach

a still completely unsatisfied existence, a kind of philosophical beast of
prey, hungry for a victim.”

As in the case of the philosophers of the enlightenment, so also in the
case of Mach, it developed that the disciples and followers displayed
an excessive tendency towards shallowness. Furthermore, to Planck’s
criterion of the fruits the present opinion provides an answer: the fruits
of Mach’s teachings are not the writings of his physical and philo-
sophical followers, but rather the enlightenment of minds brought
about by them— a fact which even Planck recognizes. By this I do not
mean to assert that Mach has no importance in other respects. I do
think, however, that this is the best summary of his position in the
general intellectual life of our times.

In this opinion I am strengthened also by the striking agreement
of his views with those of a thinker for whom he cannot have had any
great sympathy, Friedrich Nietzsche. This agreement was first pointed

” Study, op. ctt., p. 24.

Ernst Mach's philosophy of science

out by Kleinpeter.'^ The more one delves into the posthumous works
of Nietzsche, the more clearly one observes the agreement, particularly
in the basic ideas related to the theory of knowledge. Now Nietzsche
is the other great enlightenment philosopher of the end of the nine-
teenth century. The harmony of his epistemologic views with those of
Mach, who had gone through an entirely different course of instruction
and whose temperament and ethical ideals were entirely different,
seems to me to be evidence for the fact that such views must have
penetrated to the enlightened minds of that time.

That great master of language, Nietzsche, formulated these ideas
with extraordinary force and impressiveness when he said:

I behold with amazement that science today has resigned itself to being
relegated to an apparent world; a true world, be it what it may: in any case,
we have no organ of cognition for it. Here one might ask: by what organ of
cognition is one led to assume this antithesis? . . . From the fact that a
world which is accessible to our organs is also understood to he dependent
on these organs, from the fact that we understand a world as being sub-
jectively conditioned, it does not follow that an objective world is in any
case possible. Who prevents us from thinking that subjectivity is real,
essential? The “in itself” is a contradictory conception, to be sure: a "quality
in itself” is nonsense: we have the concept “being,” “thing,” always only as
a relation concept . . . The bad part of it is that’ along with the old
antonyms “apparent” and “real" the correlative judgments of value have
been propagated: “of little worth” and “of absolute worth" . .

Elsewhere Nietzsche says:

That things have a quality in themselves, quite apart from any in-
terpretation and subjectivity, is an idle hypothesis: it would presuppose
that to interpret and to be a subject are not essential, that a thing detached
from all relations is still a thing.^’

Nietzsche’s most significant expression of the positivistic world
conception is probably given in the aphorism, called “On the Psychol-
ogy of Metaphysics,” where he attacks with cutting sharpness the
employment of very frequently misused concepts:

“H. Kleinpeter, Der Fhenomenalismus (Leipzig, 1913).

“ Nietzsche, The WUl to Potver, No. 289.

“ Op. cit.. No. 291.

modern science and its philosophy

This world is apparent: consequently there exists a true world;— this
world is conditional: consequently there exists an unconditional world;—
this world is full of contradictions: consequently there exists a world that is
free from contradictions;— this world is changing: consequently there exists a
permanent world;— all false conclusions: (blind faith in the reasoning: if
there is A, there must also be its antithetical concept B )

It is not to be denied that the philosophy of enlightenment possesses
a tragic feature. It destroys the old systems of concepts, but while it
is constructing a new system, it is also already laying the foundations
for new misuse. For there is no theor)' without auxiliary concepts, and
every such concept is necessarily misused in the course of time. The
progress of science takes place in eternal circles. The creative forces
must of necessity create perishable buds. They are destroyed in the
human consciousness by forces which are themselves marked for
destruction. And yet, it is this restless spirit of enlightenment that keeps
science from petrifying into a new scholasticism. If physics is to be-
come a church, Mach cries out, I would rather not be called a physicist.
And with a parado.xical turn, Nietzsche comes out in defense of the
cause of enlightenment against the self-satisfied possessor of an en-
during truth:

The assertion that the truth is here, and that an end has been made of
ignorance and error, is one of the greatest seductions that there are. Assum-
ing that one befieves it, then the wiU to test, investigate, predict, experiment,
is crippled: the latter can itself become wanton, can doubt the truth. The
“truth” is consequently more ominous than error and ignorance because it
binds the forces with which one can work for enlighteiunent and knowl-
edge.”

Of these forces, however, at the turn of the century Mach was one
of the mightiest.

“ Op. dt.. No. 287.

” Op. dt.. No. 252.

CHAPTER

Ernst Mach and the unity of science

I N the year 1882 the famous American philosopher and psychol-
ogist William James made a tour through Europe and every-
where met scientists interested in his field of work. At the end of
October, James came to Prague and met Ernst Mach. James described
his impressions of this meeting in a letter he wrote to his wife in
America:

Mach came to my hotel and I spent four hours walking and supping
with him at his club, an unforgettable conversation. I don’t think any one
ever gave me so strong an impression of pure intellectual genius. He ap-
parently has read everything and thought about everything, and has an
absolute simplicity of manner and a winningness of smile, when his face
lights up, that are charming.

I do not want to speak here about the wide activity of Mach in
physics, physiology, psychology, and the history and logic of science, to
do which would necessitate a series of papers. Instead, I shall speak
about Mach’s activity only in so far as he may be considered one of
the spiritual ancestors of the Unity of Science Movement and, par-
ticularly, the real master of the Vienna Circle.

A hundred years after the birth of Ernst Mach we must not forget
or underrate the fact that he is still very much alive today. Surveying

the opinions of the scientific workers of today, we find many of them

* •

modern science and its philosophy

who decidedly reject his doctrine. On the other hand, there are a
great many scientists who enthusiastically express their full agreement
with him. But among the scientists who are acquainted with Mach’s
doctrine there are very few whose behavior toward him is neutral or
indifferent. In spite of this fact, opinions about what are the most
characteristic features of his doctrine are very different and sometimes
even contradictory.

On the one hand, Mach is described as the most radical opponent
of every attempt to introduce into science factors that have any tinge
of spiritual tendency. He saw even in a concept which for ages has
been in physics as usual as the concept of force a detrimental remainder
of the obsolete world picture of primitive man, which was animistic
and fetishistic. On the other hand, we are told that according to Mach
our world consists entirely of perceptions or complexes of perceptions;
that there is no such thing as matter for the building of a world. For
this reason Mach has been proclaimed as a champion of the idealistic
philosophy within modem science and a leader in the struggle against
materialism.

To hint at another difference of opinion: on the one hand, Mach is
said to claim that the sole function of science is to record observable
facts and to sum them up by economical and suitable formulas. The
scientist has, according to Mach, to be on his guard against daring
generalizations, through which an animistic or metaphysical element
may insinuate itself into science. On the other hand, physicists working
in their research laboratories accuse Mach of not recognizing the
existence of objective facts. According to these people, Mach main-
tains that there are only subjective opinions of single physicists, but no
real facts; there is no real physical world, the exploring of which was
supposed to be the goal of the research work of the physicists. For this
reason Mach’s doctrine is even alleged to have a paralyzing influence
on research work and hence on the progress of science. For only the
belief in a real, an objective, world can give to the physicist the mental
activity and force needed for his diJBBcult achievements.

"Whence these different judgments, sometimes even contradictory
to each other, about the chief lines of Mach’s philosophy? Why is the

^ Ernst Mach and the unity of science

essence of Mach’s doctrine described by different authors in such
different ways? The chief reason for these differences is, I think, that
philosophers, and sometimes scientists too, endeavor to discuss Mach’s
doctrine in the language of traditional philosophy. In this language
such terms occur as “idealism,” “spiritualism,” “materialism,” “real
objective world,” “subjective opinion of the real world.” But the point
is that it is impossible to describe Mach’s doctrine in this language, im-
possible to describe it at all in terms of traditional philosophy. If we
want to form an adequate conception of Mach’s doctrine, we must
never forget that he always declined the title of philosopher. Mach has
been praised by a great many philosophers for this modesty. But I do
not think that it was exactly modesty. He wanted rather to draw a
conspicuous boundary line between his own doctrine and the doctrine
of traditional philosophy.

Of first importance, it seems to me, for an understanding of the chief
line of Mach’s thought is a passage in the introduction of his book,
“The Analysis of Sensations,” ^ in which he explains his chief aim in
writing the papers that are commonly described as philosophic. Mach
starts from the fact that scientists are accustomed, each in his special
field, to make use of a certain system of concepts, or, to put it more
exactly, of certain technical terms, a certain technical language which
is very suitable within this special field, say physics. But this special
technical language may become very unsuitable and even misleading if
it is applied to the description and formulation of the frontier problems
which arise when we pass from one special science to a neighboring
science, say from physics to biology or to psychology. Mach’s own
words are:

1 do not claim the title of a philosopher. I want only to take, in physics,
a standpoint which does not have to be abandoned immediately when we
look over into the field of another science. For all the sciences ultimately
form a whole. What I am stating, I am perhaps not the first to state.
Furthermore, I do not want to bring forward my explanation as an ex-
traordinary achievement. I think, rather, that the same line would be taken
by anyone who tried to survey a field of science that is not too narrow.

^E. Mach, Beitrage xur Analyse der Empfindungen (Jena; G. Fischer, 1886;
English translation, Chicago, 1914). •

modern science and its philosophy

According to Mach this desire to make use of a unified mode of ex-
pression in all fields of science is a consequence of the economical
design of science. This design implies the comprehension of as many
facts as possible by the simplest possible system of propositions.

Since Mach dealt in his papers with so many different kinds of
problem in the fields of physics, physiology, and psychology, a great
many scientists did not discover what the chief trend of these papers
was. In order to find the clue to it, we have to read attentively another
passage in the same introduction. Mach says there expressly:

The basis of aU my investigations into the logical foundation of physics
as well as into the physiology of perceptions has been one and the same
opinion: that all metaphysical propositions must be eliminated, because they
are idle and disturbing to the economical design of science.

And Mach’s famous book “Mechanics and its Development’’” begins
with the sentence:

"The tendency of this paper is an elucidatory or, to put it more ac-
curately, an anlimetaphysical one.”

In the reports on Mach’s teaching by advocates of traditional phi-
losophy, one may often read that Mach’s chief doctrine was that the
world consisted of perceptions and not of material particles. But from
the passages that I have just quoted, in which Mach expressly describes
the chief aim of his investigations, it is clear that these investigations
were quite unconcerned with such problems as whether the world
consists of perceptions or of matter. This is rather the typical way in
which traditional philosophy likes to put a problem. It is just this way
of putting a problem that Mach emphatically rejected.

Hence Mach’s chief tendency may be described by the phrases,
“unification (that is, economical presentation) of science” and “elimina-
tion of metaphysics.” We shall find that these two aims are very closely
connected with each other. And we shall see that the most widely
popularized doctrine of Mach, according to which the real world
consists of perceptions, was never formulated by him in this meta-

®E. Mach, Die Mechanik In ihrer EntuHckelung (Leipzig: F. Brockhaus, 1883;
English translation, Chicago, 1893).

Ernst Mach and the unity of science

physical way. What was really in Mach’s mind when he maintained
that our world is built up of perceptions or complexes of perceptions
was not that this phrase “built up of perceptions” is in any sense a
statement concerning a property of the real world, but only that it is j
a useful means for the unification of science and the elimination of
metaphysics. It would be a misunderstanding of Mach’s aims to believe
that the construction of the world by perceptions, which was merely
a means to an end, was the true end of his philosophy. Many of his
philosophical interpreters stick fast at this means to an end, “the per-
ception language,” and neglect the real purposes of Mach’s doctrine,
the unification of science and the elimination of metaphysics. For it is
just by the presentation of some scientific results in terms of meta-
physics that the unification of science is, according to Mach, gravely
imperiled and sometimes even frustrated.

If one describes physics as the science of matter, biology as the
science of life, psychology as the science of the mind, sociology as
the science of the collective mind, metaphysical concepts or words such
as “matter,” “life,” “soul,” "collective soul,” are introduced, and it is
obvious that words like “matter” and “soul,” for example, are probably
not reducible to the same terms. It is easy to prove that the introduc-
tion of expressions of this kind renders impossible the representation of
our experiences by a unitary system of terms; in other words, it renders
the unification of science impossible.

^To remove these diflSculties Mach suggested the formulation of
the laws of physics as functional connections among perceptions such
as “green,” “warm,” “hard,” including also, of course, the space and
time perceptions. Every physical experiment consists in observing how
the alteration of some perceptions is connected with the alteration of
others. If no perceptions touching om: own bodies intervene— for ex-
ample, if there is no altering of perceptions by intoxication of our
nerves— we are in the field of physics. If we observe the connections
between perceptions, including perceptions arising from alteration in
om: own bodies, we are in the fields of physiology or of psychologyf^
But it is clear that we can no longer prove the impossibility of a unified
language of science if we start from Mach’s perception language in-

modern science and its philosophy

stead of the metaphysical terminology of traditional philosophy, and,
we must admit, sometimes even of traditional science.

On the contrai)/,% we start from Mach’s standpoint and formulate
all scientific propositions in terms of perceptions, the unification of
science becomes possible. Mach never maintained that our world
consisted of complexes of perceptions, but that every scientific proposi-
tion was a statement about complexes of perceptions. Whether it be
a proposition of physics, biology, or psychology, it can only be proved
or refuted by comparison with observation.'^

•According to Mach, the unification of science is possible, but only
by formulating all scientific propositions as propositiras about com-
plexes of perceptions, in the widest sense of this word. 'Every proposi-
tion that states something about our observations contains as predicate
some term like “green,” “warm,” “joyful,” “painful,”— perception terms,
as Carnap calls them. A proposition that is not reducible to propositions <
containing only perception terms as predicates cannot be checked by I
experience; it is a metaphysical proposition. Hence to Mach the ex-
pression “elimination of metaphysics” means the elimination of all sen-
tences that are not reducible to sentences containing only perception
terms as predicates’? The elimination from science of metaphysical
propositions leaves only sentences of a homogeneous type, namely,
sentences with perception terms as predicates. Therefore, if we demand
of science an economical representation of our experiences, that is, a
representation by a unified system of concepts, we must admit only
propositions that are reducible to propositions containing only per-
ception terms as predicates.

\This is the real meaning of Mach’s doctrine that all propositions
of science deal with perceptions. He did not want to make a statement
about the question of what the world consists of,| but he wanted to
point out how the propositions of science had to be formed in order to
make possible a unification of science. His result is this: The unifica-
tion of science is not possible except by the elimination of meta-
physical propositions.Vrhen only propositions of a homogeneous type
remain. Hence we can form from them a coherent logical system.\

The elimination of metaphysics from science was for Mach, as we

Ernst Mach and the unity of science

now understand, not a demand arising from some antimetaphysical
mood, but the only means of making possible the unification of science.
According to Mach, metaphysics must be eliminated because it is con-
tradictory to the economical function of science.

A great many people were puzzled because Mach’s philosophy,
which was supposed to be a sort of idealism (similar to the philosophy
of Bishop Berkeley), changed so easily, or— to speak in terms of ideal-
istic philosophy— degenerated so easily, into physicalism. We have seen
that even the Vienna Circle went over very quickly from the phe-
nomenal language used, following Mach, by Carnap as well as by
Schlick, to the physical language claimed by Neurath. In physicalism,
which now plays a great role in aU papers that start from the viewpoint
of logical empiricism (in the most coherent and exact way in the
papers of Carnap), a language is used that seems very near to ma-
terialism.

So it has been for a great many philosophers a riddle and almost a
source of irritation that the opinions within a group claiming to possess
a particular sense of logical consistency could oscillate so easily be-
tween the extreme poles of human thinking, which idealism and
materialism are supposed to be.

But this antithesis, which, according to traditional philosophy, exists
between materialism and idealism is not, according to Mach, a scientific
antithesis. Mach disliked the use of terms such as “idealism” and
“materialism” and if he did use them it was only to reject them.
Though he rejected materialism as well as idealism, this rejection does
not mean that he tried to take a mediating standpoint between them.
/Foi him, both idealism and materialism are systems of metaphysical
propositions, not scientific theories. For they can be neither proved nor
refuted by expeiienc^Mach had what one might call the instinctive
aversion of a genuine scientist to the use of vague terms like “idealism”
or “materialism” in science. This aversion sometimes induced bim to
make statements against one or the oBier metaphysical system. And
his statements were often misinterpreted as statements on behalf of
the other system, just as if, by rejecting one sort of metaphysics, he
advocated the contrary metaphysics. From Mach’s point of view the

modern science and its philosophy

question of “idealism” or "materialism” cannot be put as a real scientific
problem. Every attempt to exploit the achievements of science to
bolster up idealistic or materialistic metaphysics is from the beginning
doomed to failure.

What Mach felt instinctively we can today formulate in words, if
we take the standpoint of logical empiricism, as it was formulated
very precisely in Carnap’s book “Logical Syntax of Language”* and
in his paper “Testability and Meaning.” *

The transition from the supposed idealistic to the physicalistic
conception of science took place so smoothly within the Vienna Circle
because^according to the doctrine of logical empiricism, the question
to be put was not whether idealism and materialism were right opinions
about the real world, but only what language, phenomenal or physical, ^
was the more suitable for giving an economical and unitary account of
our experiences. Since either of these languages may be more suitable
within a limited field than the other, the choice of an accepted language
has nothing to do with the question whether our real world consists of
perceptions or of matter. What is of essential importance is only the
question whether we believe that it is possible to comprehend all fields
of science in one and the same language. If the unification of science,
in this sense, is held to be possible, as Carnap and the adherents
Unity of Science Movement maintain, it is of secondary importance
whether this unification be achieved in terms of perceptions, as Mach
believed and Carnap proved to be right in his first paper, “The Logical
Construction of the World,”* or whether the physical language is to
be introduced, as Carnap proclaims in his recent papers in accordance
with Neurath’s suggestions.'^

The essential alternative for our conception of science is rather this:
Do we, in accordance with traditional philosophy, maintain that the
question whether the real world consists of matter or of perceptions,
and other questions like it, are scientific questions, or do we, vrith

®R. Camap, The Logical Syntax of Language (New York: Harcourt, Bract
1937).

* Philosophy of Science (1936 and 1937).

®R. Camap, Der logiscke Aufbau der Welt (Berlin, 1928).

Ernst Mach and the unity of science

Mach, eliminate metaphysical questions of this sort from science as
disturbing its economical character and put the question just mentioned
in the way in which it is put by logical empiricism?

Then we ask, what language is the most suitable as the language of
a unified science. From this point of view, the metaphysical question
seems to be, as Mach expressed it, an idle one. And the question as logi-
cal empiricism puts it, whether the phenomenal language or the physi-
cal language is more suitable as the language of unified science, ceases
to be a question of profound metaphysical importance and becomes a
question of convenience. It is perhaps comparable to the question of
what system of symbols is the most suitable for the introduction of a
unified symbolism into logic.

If we want to describe Mach’s role in the history of human thought
and in the development of science in a particularly comprehensive
and impressive way, we can do it, it seems to me, by a clear-cut
antithesis. The traditional conception of science is connected with a
certain opinion about the importance of metaphysics to science. Ac-
cording to this conception, there are two methods of science:

(1) The first method is restricted to recording facts, including
empirical rules summarizing facts. The adherents of this method of
scientific activity take care not to introduce sweeping generalizations
and hypotheses, because by them a metaphysical element may easily
creep into science. This kind of scientific activity possesses, according
to its adherents, the advantage that all propositions admitted by science
are secured by experience or logic and are clear and intuitive. The
scientists of this group are anxious not to introduce vague phrases. But
by proceeding in this cautious way only special sciences of small extent
are created. Physics and biology and psychology have each collected a
lot of facts and rules, but there is no link between these special de-
partments. This conception of science is often referred to as the
“positivist” conception, it is not at all in accordance with the conception
of the so-called “logical positivism,” neither does it agree with Mach’s
r doctrine. This pseudo-positivist conception of science does not satisfy
our aspirations toward the unity of science.

(2) Therefore, beside this positivist conception, or more exactly,

•

modern science and Hs philosophy

over it, the metaphysical conception of scientific activity has always
existed, because it has been supposed to be better adapted to satisfy-
ing our desire for a synthesis of knowledge and the unity of science.
According to this conception we can reach the unity we are striving
after by the introduction of daring metaphysical generalizations and
hypotheses. By means of these metaphysical generalizations the
separate sciences can be summarized and unified into a unitary science.
The general principles of this unified science are, of course, metaphysi-
cal propositions. The most famous metaphysical system, which was sup-
posed to comprehend and represent all special sciences, was the system
of Hegel. In this system all separate sciences, such as mathematics,
physics, biology, are presented as steps in the self-evolution of the
absolute spirit. An example of the sort of metaphysical proposition
that serves to achieve the unification of science is Hegel’s fundamental
theorem of dialectics, namely, “every quantity, if sufficiently increased,
turns into a quality.” This theorem is supposed to be valid in physics
ns well as in biology, in biology as well as in history. It is particularly
interesting because it continues to play a great role and is not confined
to the adherents of Hegel’s idealistic metaphysics. This theorem and
many like it are taken over into dialectical materialism, the official
philosophy of the Soviet Union of today. By means of propositions of
this kind the barriers between the separate sciences are broken down
and the unification of science is achieved, but only at the price of in-
troducing large systems of very vague propositions. With regard to
such metaphysical propositions a general agreement among scientists
would never be reached.

’The opinion of traditional philosophy and traditional science has
been for ages that scientific activity has only these alternatives: either
that only theorems that can be proved by experience or logic are
recognized as legitimate in science, in which case the separate sciences
remain separated from each other by insurmountable barriers, or that
we admit the introduction of metaphysical propositions, in which case
the unification of science can be achieved, but we have to deal with
propositions that will never be recognized by all scientists.

To put it still more concisely; either the renunciation of the unifies-

Ernst Mach and the unity of science

tion of science or the introduction of metaphysical propositions into
science.

The great importance of Mach's activity lies in the fact that he
declined to recognize these alternatives. He proclaimed, rather, the
unification of science by means of the elimination of metaphysics.

It is just this phrase that is the clue to the imderstanding of Mach’s
doctrine, and of his papers, which seem to deal with so many sub-
jects and such difiFerent fields of science. What always mattered for
Mach was the opportunity to accomplish the program that we have
just outlined. And it is just this program of Mach that we may adopt
as the program of our “Unity of Science Movement,” of our Congresses
and of our Encyclopedia. If Mach’s centenary has been celebrated by
so many physicists, physiologists, psychologists, and historians of
science we may take a special pride in these celebrations, in which we
have a special right to honor him as one of the spiritual ancestors of
the “Unity of Science Movement” For, I think, within our movement,
the harvest of the seed scattered by Mach is particularly rich and in die
strictest accordance with his true intention.

CHAPTER

physical theories of the twentieth century
and school philosophy

% 1 #HAT is the significance of present-day physical theories

\i\m for the general theory of knowledge? There are many physi-
Y ycists and philosophers whose answer would be, “Nothing.”
On what grounds many philosophers give this answer, I cannot and
do not wish to investigate here. How does it happen, however— and
this question will ser\e as our starting point— that so many physicists
assert that the greatestuavol ntions in t he theorie s of physics are
.^^papgKlp nf pVia nging th fi principles ot the general theory of knowl-
edge? For example, one finds in physical works on the theory of
relativity the thesis, often defended with passion, that the relativistic
revision of the measurement of space and time has no “philosophical”
consequences.

Anyone who has occupied himself to some extent with the historical
development of physics will be struck at once by the similarity of this
thesis to what took place during the period of those great revolutions
in the theories of physics that led from the medieval, scholastic con-
ception of nature to the conception prevalent today, revolutions as-
sociated above all with the names of Copernicus, Galiledj KeplefTi'hus,
one reads that the adherents of the heliocentric theory— at that time
considered revolutionary— contended most zealously that the Copemi-

^twentieth-century physics and school philosophy

can “revolution” had brought about something that was o nly mathe -
matidallv ai^d physic ally new, that it had made no change at all in the
general philosophic conception of the world. At the famous trial of
Galileo, when pressure was brought to bear on him to recant his
doctrine, it was not a question of his swearing that he no longer be-
lieved in the motion of the earth, as one often reads in superficial
presentations, which have immortalized the famous misquotation:
“Nevertheless, it does movel” What the Inquisition actually wanted of
Galileo was only that he confess that the doctrine of the motion of
the earth was correct merely as a mathe matical &tion, but was false
as a philosophical doctrine. We can also find in the standpoint of the
Inquisition something corresponding to the modern relativistic co ncep-
tion. According to the latter, we cannot say that “in reality” the earth
moves and the sun stands still, but only that the description of phe-
nomena turns out to be simpler in a coordinate system in which this is
the case. More than this was demanded of Galile o, however. He was
expected to admit that the heliocen tric co nce p tion was a mathematical
fiction, whereas the geocentric one ytas .a. pMosaphieal ..truth. It is
readily seen that even this standpoint of the medieval authorities finds
its analogue in our times. Today, too, a fictionalistic conception is
often presented for the purpose of bringing out more strongly, by con-
trast, the “eternally vali d.” “philosophically reasonable” truths. For
instance, it is very often asserted by philosophers, and sometimes also
by physicists, that non-Euclidean geometry and the Einstein measure-
ment of time are piathematicaLfictions, whereas Euclidean geometry
and absol ute time are, in the very nature of things, established truths.

Still more often we find, however, that ^physicists refuse to make
any decisions concerning such questions as time, space, causality, pre-
ferring to leave these for the competent specialist, the philosopher or
the e;psl£0}plo.gist. Since today no one need have the same fears as
Galileo, this refusal must arise from a conviction that can be formulated
roughly as follows: “There are questions that are so profound that
they cannot be solved by the exact sciences.” In connection with this
point, some believe that there is a special method, the “philosophical,”
with the help of which such questions as those concerning the nature of

modern science and its philosophy

time, space, and causality can be answered, while others regard these
problems as forever insoluble, as “eternal riddles.”

The classical expression of this resignation of the exact sciences
was the famous speech of Emil du Bois-Reymond which dates back
to 1872 and bears the title “On the Limitations of Natural Science.” ^

This speech, which culminates in the declaration “Ignorabimus”—v/e
shall never know— has been quoted countless times— triumphantly by
the belitders of the scientific world conception, with melancholy assent
by its adherents. The speech in its essentials has been accepted by most
philosophers and scientists as irrefutable truth. In the history of the
scientific world conception it has been the scientist’s tri p to Canos sa.
If we reflect by what arguments Du Bois-Reymond arrived at his
ignorabimus, we must reach the conviction, considering the present
state of the epistemology of the exact sciences, that it is high time to
unroll the question once more, and once again to see whether the
d§spamng point of view concerni ng scientifi c , cognition is really
unavoidable.

Du Bois starts with the thesis:

The cognition of nature is the reduction of changes in the material
world to motions of atoms, acted upon by central forces, independent of
time ... It is a psychological fact of experience that wherever such a
reduction is successfully carried through our need for causality feels satisfied
■for the time being.

There still remains, however, the question of how matter is able to
exert the central forces. This question naturally cannot be reduced
again to central forces. To quote Du Bois further:

No one who has given any thought to the subject can fail to recognize
the transcendent nature of the obstacles that are here before us . . . Never
shall we know any better than today what it is that haunts the space where
matter is found. For even the spirit of Laplace could not be any wiser on
this point than we . . . Our cognition of nature is therefore enclosed by
the two boundaries set up— on the one hand, by our inability to comprehend
matter and force, and on the other hand, by our inability to understand
mental processes in terms of material conditions.

^ Uber die Grenzen de^ Naturerkennens,

% twentieth-century physics and school philosophy

If we disregard the problem of the connection between the spiritual
and the material, since it does not concern us here, Du Bois then sees
the limits of our knowledge of the world primarily in the i mpossibility
of understanding the nature of matter and force. He continues:

Within these limits the scientist is lord and master; he dismembers and
builds up; . . . beyond these limits he cannot and will never be able to go.
With respect to th e riddles of th e material world . . . ignoramus; . . .
with respect, however, to the riddle of what are matter and force, and how
they are able to think, he must decide, once and for all, on a verdict much
more di£Scult to rend er: iqnorabimus .

But what does it mean when we say that a question is insoluble?
Let us suppose, for example, that someone has asserted that the
problem of a regular transport route to the planet Neptune is insoluble,
or that the production of a living organism from lifeless matter is im-
possible. Despite this assertion, the person making it can describe quite
accurately the concrete experience we should have if the problem were
solved. We cannot, however, in any way— not even approximately—
imagine what we should have to experience in order to be able to say
that the problem of the nature of matter or force has been solved, or
that one knows, as Du Bois requires, “what it is that haunts the space
where matter is fornid.” When, for example, Heinrich Hertz, as is often
said, elucidated the nature of light, this was not at all in the sense
meant by Du Bois. According to Hertz, light and electromagnetic phe-
nomena are associated with the same equations but have different
wavelengths; the nature of light is thereby made no clearer than it was
before, since the nature of electricity is also in this sense an eternally
insoluble riddle.

Thus there are two types of unsolved and perhaps insoluble prob-
lems, which Du Bois characterizes by means of the words ignoramus
and ignorabimus. Anyone who is used to working on the real solutions
of problems will feel a certain displeasure when he turns to problems of
the second kind. For he is accustomed to proceed with the solution by
first picturing to himself the experience corresponding to the completed
solution, and then working until he succeeds in bringing about the
realization of the desired experience. If, however, we cannot state what

modern science and Its philosophy

this experience is to consist in, have we really set up a problem?

As a matter of fact, we find very often that the physicist, as physicist,
declines to work on problems set up in this way; yet in another comer
of his soul he admits that such problems might be attacked with other
methods— not physical, but “philosophical,” as they are called. In seek-
ing the reason why physicists— who as such attach the greatest value to
exact formulations of questions— in spite of their displeasure admit the
possibility of something quite different, I believe it is necessary to take
into account the fact that many physicists, when not working in their
own fields, are inclined to a world conception that has become rooted
in the educational system through centuries-old tradition, a conception
which w'e will call simply the world conception of “school philosophy.”

We do not wish to investigate here the question of why so many
physicists adhere to this school philosophy, in spite of the fact that it
was just the critically thinking physicists who contributed most to its
shaking; for the causes of this adherence are to be understood only
psychologic ally, and perhaps s ociologicall y. Rather, we wish to find out
what the standpoint of the school philosophy consists in, and how it
has made so many scientists assent without opposition to the resigned
^gnorabitnus.

It is said that the philosophic schools are so far apart from one an-
other in their points of view that it is not possible to perceive among
them anything like a unified conception_oiJhe wojld. In spite of these
individual differences of opinion, however, I believe that we can see
today a common nucleus, which has been handed down through the
centuries and, to a certain degree, has crystallized. Along with this
there has been developing, at first timidly, then more and more boldly,
but even now still quite cautiously, a new world conception, one that
is gradually gaining strength with the progress of the exact sciences. In
order to introduce some name, just as we called the traditional doc-
trine the “school philosophy,” we will call the new one the “scientific
world conception,” to indicate briefly that it recognizes no other
cognition than the scientific.

The school philosophy, whether it calls itselLxeal ism or i dealism, is
characterized by the possession of a certain conception of what is

Jwentieth-century physics and school philosophy

n alifid truth , hence also of what can be regarded as the real formula-
tion of a problem. The basic ideas of this doctrine of the school phi-
losophy cannot be presented better than by Henri Bergson’s introduc-
tion to the French translation of the American psychologist, William
James's, Pragmatism. Bergson says:

For the ancient philosophers there existed a world, raised above space
and time, in which all possible tmihsJiad dwelt since eternity. According
to these philosophers, the truth of human judgments was measured by the
degree to which they were faithful copies of those eternal truths. The
modern philosophers, to be sure, have brought down tru th from heaven .t o

would be a law governing the facts: if not ruling over them, at least ruling
in their midst; a law actually contained in our experience; it remains for us
only to extract it from the latter. Even a philosophy like that pf Kan t, which
assumes that every scientific truth is such only in relation to the human
mind, considers the true propositions as given a p riori bv human experie nce.
Once this experience, in general, is organized by human thought, the
whole work of science consists in breaking through the obstructing husk
of facts, in the interior of which the truth is housed like a nut in its shell.

earth, but they still regard it as son ^ — , , ^

ments. A proposition such as “Heat expands a body,” according to them.

✓

It is readily seen that this conception of truth permits every type
of question. It makes it difficult, however, to distinguish between
sensible and meaningless formulations of problems. For to every ques-
tion the answer can be found behind the h us k of fa cts if one bores
with sufficient energy. In principle, it might then be possible to answer
even such questions as those concerning the nature of matter and
force. If, however, the shell of the nut is so hard that it can never be
bored through, so that the answer cannot be extracted, we call the
question “eternally insoluble,” and say resignedly . Ignorabimus . If
we have this conception, we can also pose such questions as those that
are most characteristic of the school philosophy: whether the outer
world r eally exist s, and whpthf»r wr ran Imnw ths world in its t rue
properties. To these questions the realist r eplies in the affirmative, the
i dealist, in the negative. Neither can adduce any concrete experience
as decisive for his answer. Both agree, however, that su ch a giiesHnn is
a sensible problem.

modern science and its philosophy

, There is no doubt that this standpoint of the school philosophy
makes very diflBcult the acceptance and understanding of present-
day p hysical theo rips. For example, from this point of view one can
raise the question of what the “real” length of any body is. If the
[theory of relativi ty ascribe s to a body different lengths with respect to
•different reference systems, the adherent of the school philosophy will
opine that this difference arises from “perturbations” of the measuring
instrument, which make the “correct” measurement impossible in
practice. This, however, does not prevent one length from being the
“real” one as distinguished from the merely “apparent” measured
lengths. Of the f amily o f reference systems moving uniformly and
rectilinearly with relation to one another, only one can be really at
rest, according to this conception. Since according to the relativity
theory— and so far it has not been disproved experimentally— it is not
possible by any experiment to determine which is th e system that is
really at re st, for the adherent of the school philosophy this “being
really at rest” is a fact that cannot reveal itself in any concrete ex-
perience that man can have.

One who considers it obvious that an electron must have at every
instant a d efinite positiPiL-and—velocity— though the measurement of
them may be impossible— finds it difficult to understand the basic
principles of .quantum mecha nics. He is forced to interpret the
quantum-mechanical calculations, which he uses nevertheless, in
such a way that these definite positions and velocities of the electron
do not determine its future. Since, on the other hand, the doctrines
of the school philosophy in the field of mechanical phenomena re-
quire strict detennioism, he is forced to assume for the motion of
the electron some mystical vital causes, similar to organic life. True,
this conclusion will be pleasant and congenial to some people; but I
do not believe that it is useful for physical investigation. It does not
follow— as many believe— from the theories of modern physics; it arises
only from the desire to bring these new theories into harmony with the
world conception of the school philosophy.

The objection will perhaps be raised that in most of their investiga-
tions physicists are not at all concerned about philosophy, and hence

^twentieth-century physics and school philosophy

that the school philosophy cannot be a hindrance to the understanding
of relativity or the quantum theory. Physicists examine these theories
from a “purely physical” point of view and do not know anything at
all about the philosophical conception of the world. If one studies
closely the reactions of physicists toward the modem theories, how-
ever, it will be found that the less they are accustomed to thinking
about philosophical questions, the more their thinking is dominated
by the traditions of the school philosophy. Experience has also shown
that those physicists who declared, for instance, that the relativity
theory was nonsense often spoke in the name of “pure, empirical sci-
ence, free from speculation,” but took their arguments chiefly from the
school philosophy, not from empiric ism. It need not be supposed that
one has to make any philosophical studies in order to become ac-
quainted with this world conception. In all knowledge that has come
to us from the elementary school, in all metaphors of our language,
it is implicitly contained. Its presence is not noticed because traditions,
centuries old, make us take it for granted. The pure “ empiric ist” uses
it under the name “common sen se.” Hence it is no wonder that it is
just the physicist opposed to speculation who is easily inclined to the
ignorabimus of Du Bois-Reymond, with his surrender of the scien-
tific conception of nature.

There are some physicists who do not understand the “restriction to
pure empiricism” to mean that so long as one is at the experimenting
table one investigates purely empirically, but for the interpretation of
the results obtained uses “common sense,” that is, the traditional phi-
losophy. It is these physicists who are most active in the movement
against the world picture of the school philosophy. They are the physi-
cists who try in the entire realm of their world conception to admit
as an element only that which has been concretely experienced, as
every physicist does at the experimenting table.

These critically thinking physicists must ask themselves: how are
those problems constituted the solutions of which represent advance-
ment, as compared with the problems in the investigation of which
scientists have been, figuratively, rotating about their own axes for
centuries?

modern science and its philosophy

For example, in the past the identity of light and electromagnetic
radiation was not known, and now it is known. What does this sig-
nify? By means of electrical devices— for example, radio transmitters
—and by means of light sources one can produce phenomena that obey
the same formal laws, the wave laws, and are differentiated by only
one quantity, the wavelength. This recognition of the identity of light
and electromagnetic radiation can be expressed as a perfectly definite
statement concerning concrete experiences. It is not at all necessary
to express it in such a way that something is said about the “nature” of
light or electricity. Definite rules assign to the electromagnetic experi-
ences symbols, the field quantities, among which there exist formal
relations, the field equations. From given combinations of symbols
one can then, using mathematical operations, derive new combina-
tions with the help of the equations. These combinations may be trans-
lated into experiences again with the help of the same rules of assign-
ment. Hence, with the help of the theory, which consists of rules of
assignment and of field equations, one can draw conclusions about future
or past experiences on the basis of given experiences, In this way one
has practical control over the experiences. Identity of light ind elec-
tricity then means an identity of mathematical relations between sym-
bols. From the theoretical point of view, the solution of a problem
means the assignment of symbols to experiences, among which there
exist relations that can be stated. From the more practical point of
view, it means the possibility of obtaining control over one’s experi-
✓ences with the help of this system of relations.

easier for us to control them. Truth cannot be sought nf our

experiences. The aim of the investigation is not the seeking after a

“l yality. hidden in a nnts>|c ll ” The edifice of science must be built up
</out of our experiences and out of them only.

Before I go further into a discussion of how much the present physi-

^Iwentieth-century physics and school philosophy

cal theories require such a conception of science, I should like to show
with the help of a few historical remarks how the edifice of the school
philosophy was gr adually underm ined, and what new conceptions have
taken its place. As this development is still in its beginning stage, I shall
have to give a somewhat aphoristic presentation rather than a sys-
tematic one.

In the city of Prague there lived and wrote the physicist who led
most determinedly the struggle against the conceptions in physics
that correspond to the reality concept of the school philosophy. Erns t
Mach t aught in Prague from 1867 to 1895, that is, from his twenty-
ninth to his fifty-seventh year. He was professor of experimental
physics, first at the then bilingual University of Prague, and after the
separation, at the German University. Here he wrote those of his
works that are most important f or the epistemology of physi cs; “The
History and Root of th e Principle of Cons ervation of Energy” (1871),*
and “Mechanics in its Development” (1883).*

His fundamental point of view was that all principles of physics
are principles concerning the relations between sense perceptions,
hence principles that state something a bout concrete experien ces. All
concepts such as atom, energy. forc B, and matter are, according to
Mach, only auxiliary concepts, allowing one to make statements about
sens e perceptions in a simpler and more syn ogti Ejorm. tban if they were
formulated directly as statements about the perceptions. In this way,
all questions concerning the nature of force, matter, and so on, be-
come meaningless, for these concepts can be eliminated from all physi-
cal statements so that only statements about concr ete experiences ar e
left. The ignorabimus toward the question of the n ature of matter and
force, according to this conception, has no more justification than if a
mathematician were to say: "Science, to be sure, can set up aU the
theorems about complex numbers, but it will never be able to explain

^Die Oeschichie tmd die Wurzel des Satzes von der Erhaltung der Arbeit,
tr. by Philip E. B. Jourdain as History and Root of the Principle of the Conservation
of Energy (Chicago: Open Court I^hlishing Co., 1911).

’ Die Mechanik in threr Entioickelung, historisch-kritisch dargestellt, tr. hy
Thomas J. McCormack as The Science of Mechanics (Chicago: Open Court Pub-
lishing Co., 1803).

modern science and its philosophy

For example, in the past the identity of light and electromagnetic
radiation was not known, and now it is known. What does this sig-
nify? By means of electrical devices— for example, radio transmitters
—and by means of light sources one can produce phenomena that obey
the same formal laws, the wave laws, and are differentiated by only
one quantity, the wavelength. This recognition of the identity of light
and electromagnetic radiation can be expressed as a perfectly definite
statement concerning concrete experiences. It is not at all necessary
to express it in such a way that something is said about the “nature” of
light or electricity. Definite rules assign to the electromagnetic experi-
ences symbols, the field quantities, among which there exist formal
relations, the field equations. From given combinations of symbols
one can then, using mathematical operations, derive new combina-
tions with the help of the equations. These combinations may be trans-
lated into experiences again with the help of the same rules of assign-
ment. Hence, with the help of the theory, which consists of rules of
assignment and of field equations, one can draw conclusions about future
or past experiences on the basis of given experiences. In this way one
has practical control over the experiences. Identity of light ind elec-
tricity then means an identity of mathematical relations between sym-
bols. From the theoretical point of view, the solution of a problem
means the assignment of symbols to experiences, among which there
exist relations that can be stated. From the more practical point of
view, it means the possibility of obtaining control over one’s experi-
✓^nces with the help of this system of relations.

We see then that in no problem of this sort is it ever a question
of bringing about an “agreement between thought and object,” as the
school philosophy says. Rather, it is always only a question of inventing
a procedure which, with the help of a skillfully chosen system of sym-
bols, is capable of bringing order into our experiences, thus making it
easier for us to control them. Truth cannot be sou ght nntsidp-o f our
experiences. The aim of the investigation is not the seeking after a
“reality, hidden in g niifubpll ” The edifice of science must be built up
»/out of our experiences and out of them only.

Before I go further into a discussion of how much the present physi-

^Iwentieth-century physics and school philosophy

In the city of Prague there lived and wrote the physicist who led
most determinedly the struggle against the conceptions in physics
that correspond to the reality concept of the school philosophy. Erns t
Mach t aught in Prague from 1867 to 1895, that is, from his twenty-
ninth to his fifty-seventh year. He was professor of experimental
physics, first at the then bilingual University of Prague, and after the
separation, at the German University. Here he wrote those of his
works that are most important f or the epistemolo g y of physi cs: “The
History and Root of the Principle of Conservation of Energy” (1871),®
and “Mechanics in its Development” (1883).®

His fundamental point of view was that all principles of physics
are principles concerning the relations between sense perceptions,
hence principles that state something a bout concrete experien ces. All
concepts such as atom, energy, force, and ma H-er are, according to
Mach, only auxiliary concepts, allowing one to make statements about
se nse perceptions in a simpler and more syno pt ic J ornu than if they were /
formulated directly as statements about the perceptions. In this way,
all questions concerning the nature of force, matter, and so on, be-
come meaningless, for these concepts can be eliminated from all physi-
cal statements so that only statements about concrete experiences ar e
left. The ignorabimus toward the question of the natu re of matter and
force, according to this conception, has no more justification than if a
mathematician were to say: “Science, to be sure, can set up all the
theorems about complex numbers, but it will never be able to explain

Geschichte und die Wurzel des Seizes von der Erhaltung der Arbeit,
tr. by Philip E. B. Jourdain as History and Root of the Principle of the Conservation
of Energy (Chicago; Open Court Publishing Co., 1911).

® Die Mechanik in ihrer Entwickelung, historisch-kritisch dargesteUt, tr. by
Thomas J. McCormack as The Science of Mechanics ( Chicago; Open Court Pub-
lishing Co., 1893).

modern science and its philosophy

the nature of the complex number. Toward this problem we must
modestly acknowledge an eternal ignurabimus." To this contention
every other mathematician will respond that the complex numbers
have been introduced only in order to make clearer certain statements
about real numbers, that basically every theorem from the theory of
functions of a complex variable can be expressed also as a theorem
about real numbers.

Neither Mach himself nor his immediate students has systematically
carried further his point of view and set up, in opposition to the world
conception of the school philosophy, a similarly coherent scientific con-
ception. On the contrary, Mach’s teaching, through many presentations,
has been washed out into something indefinite rather than built up to a
consistent scientific conception of the world. It has even been inter-
preted again in line with the school, philosophy, sometimes more re-
alistically, sometimes more idealistically, so that to many— as, for ex-
ample, to the great anti-Machi stic school in Russia, at the head of
which stood Lenin himself— it appeared not as the beginning of a new
scientific world conception but as a new fashionable form o f the school
philosophy.

Conceptions similar to those of Mach were presented in France, in
part independently, by the physicist Pi erre Duh em. In his expositions,
Qubem did not equal Mach in breadth of vision, but often surpassed
him in sharpnes^_gfJogic.

From an entirely different direction there arose against the school
philosophy a movement often referred t o as “conventionali sm." Its most
important representative is the French mathematician, physicist, and
astronomer, Henri Poincar e. He called attention to the fact that physi-
cal principles often contain concepts that are defined by these very
principles. In such cases the principles can never be tested against ex-
perience, since they are disguised definitions, “conventions.” Thus, ac-
cording to Poincare, the law of conservation of energy is nothing but a
definition of the concept of energy . The significance of conventionalism
for the understanding of what is expressed by the principles of physics
is very great, in my opinion, and perhaps no one among the physicists
has contributed as much as Poincare to the shaking of the school phi-

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^twentieth-century physics and school philosophy

losophy. In Germany the chief representative of this movement is Hugo
Dingier. Through extreme application of conventionalism, however,
Dingier has again approached the school philosophy, according to the
principle that opposites meet, by attempting to show that certain con-
ventions are the simplest and hence are the only ones justified.

A direct attack against the truth concept of the school philosophy
was made by the American psychologist William James in his boo k
Pragmatis m, which introduced the pragmatic movement that has spread
so vwdely. According to James, the truth of a system of principles— a
physical theory, for instance— does not consist in its being a fa ithful copy
of realit y, but rather in its allo wing us with th e help of_&es e principle s
to change our experiences according to our wishes. According to this
view, which essentially agrees wiA that of Mach, but rejects even
more bluntly the truth concept of the school philosophy, every solution
of a problem is the constructionof a proced ure that can be of use to us in
the ordering and mastering of our experiences. If, for example, we are
familiar with all the means and rules of machine construction, if we
know what motion takes place under given conditions, then it is clear
that it would not help us further in the slightest if we knew, besides this,
the nature of matter and force. If we understand the solution of a prob-
lem in the sense of James, then we cannot, in general, consider ques-
tions like the latter as scientific formulations of problems.

Henry Bergson, in his introduction to the French translation of
James’s Pragmatism, from which we have taken the characterization of
school philosophy, also characterizes very clearly and pertinently the
contrasting pr agm atic conce pHnn nf truth and

The other conceptions [those of the school philosophy] represent truth
as something that was present before the w ell-defined act of the man who
formulated it for the first time. We say he was the first W see it, but it had
been waiting for him as America had waited for Columbus. Something had
hidden it until that moment from all eyes, had covered it, so to speak, and
he had discovered it. Quite different is the conception of William James.
He does not deny t hat reality ^ at least to a large extent, is independent of
what we say or think. But truth, which can only be associated with what we
state about reality, appears to him to be created by our statement. We in-
vent truth in order to make reality useful to us, just as we create mechanical

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modern science and its philosophy

devices in order to make the forces of nature useful to us. It seems to me
that one might summarize the essence of the pragmatic conception of truth
in a formula of the following kind: Whereas for th e other conceptions a
new truth is a discovery, fnr pragmatism it is nn invpntinn

The objection has often been raised that pragmatism correctly char-
acterizes only the practical, not the theor etical, significance of science.
To this objection James himself replied that next to the interest that man
has in breathing freely his greatest interest, which in contrast to most
interests of a purely physical kind knows no fluctuation and no failure,
is the interest in feeling that he is not contradicting himself, that what he
thinks at the present moment agrees with what he thinks on other oc-
casions. As we shall soon see, however, unambiguity or freedom from
contradictions is the most essential attribute of every cognition; hence,
confiicts between the practical and theoretical conceptions of truth do
not arise from the doctrine of pragmatism.

The physicist in his own scientific activity has never employed any
other concept of truth than that of pragmatism. The “agreement of
thoughts with their object,” as the school philosophy requires, cannot be
established by any concrete experiment. In practice we encounter only
experiences, never an object; hence nothing can be compared with an
object. Actually, the physicist compares only experiences with other ex-
periences. He tests the truth of a theory through what one is accus-
tomed to call “agreements.”

Thus, for example, one always obtains the same numerical value
for the Pl anck constant h . using various methods. This really means that
the quantity h can be constructed in entirely different ways from experi-
ences— as from the experiences of black-body radiation, or those of the
Balmer series of the hydrogen spectrum. The theory in which h plays a
role then asserts that all the various groups of experiences, which are
qualitatively so different from one another, nevertheless should give the
same numerical value of h. It is therefore only a question of comparing
experiences with one another. This procedure, which the physicist is ac-
customed to use in his work, has been made by Mach and James into a
general conception of the criteria of trutji.

In all this it must be admitted, however, that these conceptions pos-

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twentieth-century physics and school philosophy

sess a certain indefiniteness for the mathematical physicist. He always
has the impression that there is a lack of precision. In particular, he
finds it hard to take the pragmatic theory of truth quite seriously. This
arises partly from the fact that James, and to a certain extent Mach also,
failed to set a very high val ue on the role of formal logic in the cnnst mc-
tion of the system of human cognition. In fact, in a certain opposition
to the misuse of logic by school philosophy, they both emphasized the
fluid elements in cognition as against the rigidly logical. Another way
of putting it is that, in opposition to the viewpoint of mathematica l
logic, which to them always smacked of the school philosophy, they
presented the viewpoint of evolutionarY biolo gy. Because of this the
mathematicians and mathematically thinking physicists have often been
forced into a certain opposition to the doctrines of Mach and James.
Many of them, attracted by the logical garments of the school philos-
ophy, have even behaved in a friendlier way toward the latter than
toward the modem tendencies.

It is therefore significant that the school philosophy has also been
criticized from quite another side; indeed, that position was assailed
which seemed most unassailable, namely, the logic of the school phi-
losophy. The logic employed by philosophers until well into the nine-
teentn century was not very different from that formulated bv Aris -
totle. In connection with the investigations on the foundations of
mathematics, however, there developed in the field of logic a fresh
tendency, which shook the old s cheme of Aristo tle. This movement is
represented in Germany, especially, by the names of Schroder, Freg^
and Hilbert. Through the use of a symbolism modeled afrp.r that nf
mathematics it gave to logic ^ flex ibility_and_ free dom of ino vement
that it had not possessed before. This made it possible to deal with far
more complicated thought structures than could have been handled
on the basis of the school logic.

It turns out, in fact— and this is chiefly the work of the English ,
mathematician and logician Bertrand Russell and his students, par-
ticularly the Austrian Wittgenstein— that the logic of the school philos-
ophy, because of the narrowness of its sc heme, made it impossible
from the very start to express certain thoughts. Thus, many of the

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modern science and its philosophy

principles regarded by the school philosophy as being certain were
certain only because the contrary did not fit into the scheme of Aris-
totelian logic.

In this way Russell pointed out that one of the most fateful er-
rors of the school logic was its assumption that every judgmen t con-
sists in attributin g^ to a sub j^^*^ pmpprty as_prfidicat:e. If one says,
for example, that a body A is moving with respect to another body B,
the adherent of the school logic will demand that to one or the other
of the two bodies shall belong the predicate of motion. Now Russell
has shown that very many judgm ents-consist i n stating a r elat ion be-
twee n twn things a nd cannot be r educed to the statement of a property
of a single thing, which is a much more special case. However, to the
adherent of the s^ool logic a statement like the following, for ex-
ample, appears nonsensical: “If two bodies are moving with respect
to each other, it is meaningless to ask which one is ‘really’ moving, that
is, to which one belongs the predicate ‘being in a state of motion.’ ”

With regard to the school philosophy, which has taken over the old
logic more or less consciously, Russell remarks that it is led by the
unconscious conviction that all statements of judgments must have the
subject-predicate fo rm— in other words, that every statement must at-
tribut e a property ta .a_thing. This conviction has made most philoso-
phers incapable of understanding the wo rld of science and of everyday
life. According to Russell, however, most philosophers are less con-
cerned with attaining ^ true under standin g tlii&- w orld than with
showing its unreality in the interest of a transcendental, truly real
world.

With the aid of the old logic the school philosophy could easily
deduce the absurdity of the pragmatic concept of truth and the rela-
tivistic conception of physics. On the other hand, the ne y logic of Rus-
sell and his school was suitable to help build up th e pmely empiri cal,
and hence still somewhat vague, conceptions of Mach and James into a
real system of the scientific world conception that was superior to the
school philosophy from the standpoint of f ormal logic as well.

’There were some philosophers with a mathematical-physical orien-
tation who followed Russell but at the beginning cared little for Mach

twentieth-century physics and school philosophy

and almost nothing for James. Nevertheless, like the latter, they too
discarded the truth concept of the school philos ophy. In contrast to
the method of jj^n ^tism . however, they not only tried to characterize
the system of science in a general and somewhat indefinite way by
saying that the system is an instrument to be invented and constructed
in order to find one’s way among experiences, but also— and instead—
they investigated the structure of this instrument. The investigation
took place through an analysis of the method by which physics orders
the experiences through a mathematical system of formulas. From this
most advanced science, as an example, one can get an insight into the
requirements that must be imposed on scientific cognition in general.

What then are the elements of which the instrument that we call
science or cognition is composed? Here the infiuence of the mathe-
matical-logical movement becomes felt. The new epistemology says
that the system of sciencb'^nsists of symbols. This conception has
been most clearly formulated by Moritz Schlick i n his “General Theory
of Knowledge.” * Lik e Jame s, Schlick begins with a determined rejec-
tion of the jruth concept of school philosophy. He says that

in the past, the truth concept was almost always defined as the agreement of
the thou ght wit h its objects.

He then shows that the word agreement” cannot mean here anything
like equality or similarity, as in ordinary usage, since between a judg-
ment and the circumstances that it judges there can be no similarity.
He continues:

Thus the concept of agreement melts away before the rays of analysis,
in so far as it is to mean equality or similarity; and what is left is only a
unique correspondence. In diis consists the relation of the true judgment
to reality, and all those naive theories according to which our judgments
and concepts somehow could portray reality are completely destroyed.
There remains for the word "agreement” no other meaning than that of
unique correspondence. One must dismiss the thought that a judgment in
relation to the facts of the case could be anything more than a symbol, that
it could be more intimately connected with them than through mere cor-
respondence, that it is able somehow to describe or express or portray them

*M. Schlick, Allgemeine ETkenntnislekre (Berlin: Springer, ed. 2, 1925).

105

modern science and its philosophy

adequately. Nothing like it is the case. The judgment portrays the nature
of what is judged as little as the note the tune, or as tlie name of a man
his personality.

If a person had always known and kept in sight the fact that cognition
arises simply through an assignment of symbol to object it would never have
occurred to him to ask whedier it is possible to have a cognition of things
“as they really are” themselves. He would be led to this problem only by
the opinion that cognition is a kind of pictorial representation that portrays
the things in one’s consciousness. Only under this assumption could he ask
whether the images really have the same qualities as the things themselves.

It is easy to convince oneself that physical cognition consists in
the unequivocal assignment of a system of symbols to experiences.
Thus, for example, to electromagnetic phenomena are assigned field
intensities, charge densities, and material constants as symbols. Among
these symbols there exist formal mathematical relations, the field equa-
tions. Symbols that are equivalent to one another according to these
relations or to the general logical and mathematical laws can be as-
signed to the same experiences without violating the uniqueness in the
required sense.

If, for example, we start with a definite measured distribution of
electric charge on the surface of a sphere, there is assigned to this ex-
perience, as a symbol, a definite mathematical function— the charge
density as a function of position. If the sphere is left alone and we ex-
amine it after a lapse of some time, we measure everywhere the same
charge density. To this experience is assigned a constant number for
the density. If now the field equations were so constituted that accord-
ing to them there would be obtained for the calculated charge density
after some time a function other than a constant, then we should have a
symbol system that would assign to the final electrical state of the
sphere various symbols that are not equivalent. Because of this am-
biguity we should say that our symbol system, which on the one hand
is based on the rules of assigning symbols (here it is the method of
measuring electric charges), and on the other hand on the relations
among the symbols (here the field equations), gives no true cognition
of the electrical phenomena.

Every verification of a physical theory consists in the test of whether

^entieth-century physics and school philosophy

the symbols assigned by the theory to the experiences are unique. If,
for example, the Planck constant h occurs in the equations, it denotes
a definite experience. This can be produced concretely if by means of
the equations we express h through so-called “observable” quantities,
that is to say, those symbols to which our rules assign concrete experi-
ences. In this way an experience is then directly assigned to the quan-
tity h. As is well known, one can express h through quantities con-
nected with the observation of black-body radiation and through
quantities that arise from the observation of the Balmer series in the
hydrogen spectrum. There are thus two experiences apparently de-
noted by h. These consist in the calculation of its value from two dif-
ferent groups of phenomena. If the two gave different values for h,
we should be denoting two entirely different experiences by the same
symbol h. We should then have in the system of equations involving
h, in conjunction with the rules of assignment (methods of measure-
ment), a symbol system that does not denote the experiences uniquely,
and hence represents no true cognition. Through the fact that they both
do give the same value of h we recognize the uniqueness of the sys-
tem, of symbols, the “truth” of the theory.

This comparison of the values of a quantity, calculated in different
ways from observations, is the only way in which the physicist in his
actual work can test the “truth” of a theory. The direct comparison of
“observed” and “calculated” values, as it is often called in works on
physics, turns out on closer examination to be nothing else than the
test of the uniqueness of a symbol system. Suppose, for example, that
on the one hand I calculate a current strength from the electronic the-
ory of metals, while on the other hand I “observe” a galvanometer.
Then this alleged observation is also only a calculation from another
theory, namely, that of the galvanometer. For in reality I observe only
the coincidences of pointers and scale divisions, and even these sub-
stantiations on more careful analysis would turn out to be results of a
theory of the solid body. Even in the limiting case, where a value “is
observed as directly as possible”— for example, if it is a question only
of the position of a pointer on a scale— it is still calculated from the
theories of rigid bodies and light rays, because I observe directly only

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modern science and its philosophy

dancing spots of color and not positions of the pointer. Hence what I
usually call the comparison of observed and calculated values is, for
example in our case, the comparison of the values of currents given
from two different theories for the same concrete experience.

The school philosophy interprets an agreement of this kind—
which, we are convinced, is the only criterion of truth for tiie physicist
—in the following way: If for a quantity, for example, h, the same
numerical value is obtained in various ways, then this quantity has a
real existence. If by this expression is understood only what was
really substantiated, namely, that the quantity h occurring in the equa-
tions can be calculated uniquely from phenomena of various kinds,
then no objection can be raised against it. However, we must not say
then that from the agreement of the results of the measurements we can
draw conclusions about the real existence of h; for in that case this
existence is identical with agreement.

Similarly, no conclusion drawn from physical experience concerning
the real existence of the quantum of action, the elementary charge of
electricity, or similar concepts, is a scientific conclusion. It finds its
justification only in the metaphysical representation of reality given
by the school philosophy, according to which the true principles exist
before all experience and must be discovered by investigation, as Co-
lumbus discovered America.

1 believe that the mathematician can get from the following il-
lustration a very good understanding of the difference between the
school philosophy, which recog nizes metaphysical reali^T and the sci-
entific world concepti on, which uses only constructions based on con-
crete experiences.

If I have a convergent sequence of rational numbers, having an
irrational number as a limit, I can establish a convergence without
making use of the concept of the irrational number. That is to say, I
need only to establish that the difference of any two rational members
of the sequence above a given index can be made arbitrarily small by
choosing an index that is suflBciendy large> I have therefore before me,
if I have defined only the concept of the rational number, a sequence
of rational numbers having the property of convergence, but no limit

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twentieth-century physics and school phiiosophy

in the domain of rational numbers. As is clear to every mathematician,
there is no conclusion by the help of which it could then be shovm
that a limit of this convergent sequence exists. Rather, the convergent
sequence itself is the concrete exhibitable object. However, I can now
define such a sequence as an irrational number. This means that in all
theorems involving irrational numbers I can substitute for the latter,
sequences of rational numbers. It is not necessary, and is not justifiable
logically, to speak of a real existence of irrational numbers, inde-
pendent of the rational ones.

If we take this as an analogy, then the concrete experiences cor-
respond to the rational numbers and the so-called really existing truths
to the irrational numbers. A group of experiences with a system of
symbols assigned to it, in which such agreements can be established
throughout as we established in the case of the constant h, for example,
corresponds to a convergent sequence of rational numbers. The
uniqueness of the symbol system can be established within the group
of experiences itself vidthout having recourse to an objective reality
situated outside, just as the convergence of a sequence can be estab-
lished without the need of discussing the limit itself.

Likewise, as the concept of the irrational number is first defined by
the convergent sequence of rational numbers, so the concept of true
existence, say of the quantum of action h, is first defined by the agree-
ments in the whole group of experiences involving h.

Just as the expression “irrational number” is an abbreviation for a
convergent sequence of rational numbers, so the concept of a really
existing quantum of action is only an abbreviation for the group
of experiences which yield one and the same numerical value
for h.

It is completely false to say— as is often said— that the agreements
of the values of h are explained most naturally by means of the hypothe-
sis of the real existence of a quantum of action. In a hypothesis one can
only state a conjecture about future experiences, not about the “real
existence” of a thing corresponding to an assigned nam^To state a
conjecture of this kind would be exactly as if a mathematician were to
say: “The existence of convergent sequences of rational numbers with-

109

modem science and its philosophy

out limits can be explained most naturally by means of the hypothesis
that there are irrational numbers.” In reality, through such an asser-
tion he would only be giving a new name to convergent sequences
without limits. Similarly, through the assertion of the existence of a
quantum of action no new fact is stated besides the agreements. Hence,
also, no hypothesis is present,

I have already spoken about the fact that the development of the
scientific conception of nature was retarded by a certain conflict be-
tween the mathematical-logical and the biological-pragmatic approach.
The latter was greatly lacking in precision, so that even the school
philosophy appeared to have many advantages here. Thus, for ex-
ample, Bertrand Russell in his book. Our Knowledge of the External
World‘ in many points showed greater concurrence witli the concep-
tions of the school philosophy than with those of Ernst Mach. In the
German translation of this book, however, Russell remarks in a foot-
note that he now agrees with Mach on one of the most important
points. It seems to me that in the case of other representatives of the
Russell movement as well the conviction is gaining ground that a con-
sistent further expansion of the scientific world picture is not to be
sought by opposing the Mach conception in favor of the school phi-
losophy for the sake of its apparently more rigorous logic. On the con-
trary, it appears that this expansion must be carried out with the aid
of modem logic by building up the doctrines of Mach to form a sys-
teip everywhere free from objections on logical grounds.

Although according to modem conceptions logic can produce
nothing more than tautological tran.sfo rmations of principles, it is
nevertheless indispensable for the construction of a rigorously scientific
world picture. The reason is that many of the prejudices of the school
philosophy arose from the fact that me re tautologie s were regarded
as expressions of cognition. A complete survey of all possible tautologi-
cal transformations therefore offers the possibility of constmcting on
the basis of Mach’s views a scientific edifice that is superior to the
school philosophy in its logical precisiom

'The most determined attempt in this direction was undertaken by
' Chicago: Open Cou^ Publishing Co., 1914.

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twfentleth-century physics and school philosophy

Rudolf Carnap. In his book “The Logical Structure of the World,”*
which appeared in 1928, he seeks to build up the whole system of
science, starting from concrete experiences. He tries to show that all
principles in which p hysical or psychologica l objects are inyolyed can
be replaced by statements concernin g concrete experi ences. The rules
according to which statements about concepts must be replaced by
statements about concrete experiences are called by Carnap the con-
stitution of these concepts. In a scientific statement there should occur
only concepts the constitution of which is known. The basis of eyery
science is the system of concept constitutions. The building of this
system step by step with the help of the modem lope o f Russell is*^
w^t Camap calls the logical structure of the world.

' According to this conception, a scientific problem can consist only
^in asking whether a definite scientific statement is tme or fals e. Since,
howeyer, eyery such statement can be reduced to a statement about
concrete experiences if the constitution of the concepts occurring in
it is known, eyeiy problem that can be called scientific consists in the
question whether a definite relation among concrete experiences does,
or does not, exist. At the same time Camap shows further that all rela-
tions, in the last analysis, can be reduced to statements of a similarity
between concrete experiences. Since one can properly assume that
eyery such similarity is confirmable in principle, it follows that eyery
problem that can be scientifically formulated is also soluble in prin- ^
ciple. '

We see that the consistent carrying through of a piurely scientific
world conception, as attempted by Camap, leads us just as far away
from the resigned ignorabimus as does the pragmatism of James,
which is thought out somewhat less logically but in its tendencies has
the same goal. Camap formulates it thus:

Science, the system of conceptual co^^on, has no limitations . . .
There are no questions the answers to which are impossible for science in
principle . . . Science has no boundary points . . . Eyery statement
formed ^from scientific concepts can be established in principle as tme
or false. ,

*R. Camap, Der logische Aufbau det Welt (Berlin, 1928).

Ill

modern science and its philosophy ,

( This does not mean, of course, that there are no other domains of
life than science. These domains, however— lyric poetry, for example-
are distinct from science. Through the latter itself no problems can be
set up that are insoluble by its means.

Wittgenstein says very precisely;

an answer cannot be expressed, neither can the question be

expressed.

Hence, as understood by Carnap and Wittgenstein, the questions
beloved by the school philosophy, such as whether the outer world
really exists, not only cannot be answered but cannot even be expressed,
because neither the positive assertion, falsely called the realistic
“hypothesis,” nor the negative idealistic assertion can be expressed
through constituted concepts. In other words, neither assert ion can be ,
expressed as a substantiable relation among concrete experiences. We
see here the close relationship betwe n the truth concept of the m odem
l ogical movement and that of prag matism.

A tendency similar to that of Schlick and Carnap is followed by
Hans Reichenbachj but Reichenbach departs from Carnap in many
points, as in the recognition of the realistic stan dpoint.

After this survey of the movements that seek to construct a purely
s cientific world conception through following closely the actual prac-
✓• ^ce of mathe matical and physical investigati on in contrast to the school
philosophy, let us return to our starting point, the question of why
physicists often refuse to pass judgment on problems like spa ce, time,
and causality, and leave them to the philosophers.

This refusal, we can now say, arises from the fact that these physi-
cists, consciously or unconsciously, cling to the doctrines of the school
philosophy, according to which such problems must be solved by
methods fundamentally different from those employed by physicists.

If a scientist follows these thoughts through logically, he must end up
in the blind alley of ignorabimusT^

If, however, we stand on the ground of the purely scientific world
conception, we know that the solution of a scientific problem can only
consist in finding out new relatio ns among concrete exp eriences, or.

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twentieth-century physics and school philosophy

to express it in another way, in making progress in the unique designa-
tion of experiences by a system of symbols.

One can try to fit new experiences into places in the existing sys-
tem of symbols; this we call purely experimental investigation. The
idea that there can be a still pmer type of experimental investigation
that makes no use at all of symbol systems is, in my opinion, an illu-
sion.^To be sure, as Schlick properly points out, one can experience
phenomena and can get to know them without using any symbol sys-
tem; but this is not scientific cognition. For, at best, one could then
establish, for example, that today about noon several colored spots were
seen in certain combinations, although a more exact analysis would
probably show that even in such an utterance there is already an as-
signment of symbol to experience.

The work of the theoretical physicist consists, in part, in investigat-
ing the consequences resulting from the fundamental relations be-
longing to the symbol system. This is an essentially mathematical task,
such as, for example, the integration of the field equations, the funda-
mental relations among the field quantities. Another part of the work
of the theoretical physicist consists in extending the symbol system.
Naturally, with the introduction of new symbols new rules of assign-
ing them to experiences must also be introduced.

If, for example, in the investigation of the hardness of a substance
one must make a new hypothesis concerning its crystal lattice, this
means a change in the symbol system; specifically, in the geometric
figure by which the substance concerned is characterized. Everyone
will acknowledge that a work of this kind is really a concrete physical
work. From such changes in the symbol system there extends a con-
tinuous series to those changes that the physicist often feels to be
“speculative” or “philosophical,” as, for example, the introduction of
the Einstein time scale. Here, too, the question is only one of setting
up a new rule of assigning the symbols t and If in our equations to
our experiences, as well as of a new relation between the symbols
f and If in the symbol system. One can give no criterion, however, to
determine whether a change means a physical cognition or a philo-
sophical one. For the physicist there exist no such limitations. Whether

113

modern science and its philosophy

I am dealing with the measurement of hardness or with that of space
and time, it is always only a question of assigning a unique system of
symbols to experiences. Nowhere is there a point where the physicist
must say: “Here ends my task, and from here on it is the task of the
philosopher.”

This could happen only for a thinker standing on the ground of the
school philosophy. He might ask, for example: “When I have exhausted
all problems of assigning time symbols to experiences, which among
the time scales admitted by the relativity theory is the true, real time?”
And that question the physicist cannot answer; it is the philosopher
who must pass judgment on it.

It looks as if classica l physics ha s been living on good terms with
school philosophy, whereas modem physics, with its relativity theory
a nd quantiiTn mechanic s- has at once come into conflict with it. The
physicists who feared the break with school philosophy could resolve
this conflict only by a kind of doctrine of double truth. They said, in
effect; “We physicists speak on ly of time- measurements; hence for us
the relativity theory is valid. The philosopher speaks of t he real
time; for him perhaps something else is valid.” If this doctrine of
d ouble truth wa s meant somewha t ironcially, as was often the case,
it was an irony of embarrassment. There are actual cases, however,
when it is meant in all seriousness.

The reason that the conflict did not occur during the time of classical
physics is simply that, for example, the time concept of the school
philosophy had just as much an empirical physical origin as that of the
relativity theory, the difference being that the former corresponded to
the o lder state of physics, that which we today call the classical. The
symbol system with the help of which Newtonian mechanics and
Euclidean geometry portrayed space and time experiences was de-
clared by the school philosophy to b e real s pgf^p anfl Hmf»^ and pro-
claime d as eternal tru th.

If, however, in accordance widi the scientific world picture, we
regard every problem as merely one of assigning symbols to experi-
ences, then in the designation of the space and time experiences a
change is fully as possible as in the rest of physics. Just as this leads to

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twpntieth-century physics and school philosophy

progress in the theory of the solid body, so it also leads to progress in
the study of space and time, keeping up with the progress of our
observations.

One cannot declare certain parts of the symbol system to be un-
changeable for all time. To be sure, one may keep the old Kantian
• terminology, in a certain sense, and explain space and time as the
frames of physical phenomena. But one must bear in mind, as Reichen-
bach correctly says, that this frame, too, must be always adapted more
and more closely to our progressing expIfiSice.

The rise of the physics nf Galileo and Newt on brought about the
breakdown of the philosQoh v- of Aristo tle, which attempted to show the
eternal truth of the physios of antiquity. Similarly, beside the relativity
t heory and quantum^ meoh anics there cannot e.xist a philosophy that
contains a fossiliza tion of jhe yi grlier phys ical theories.

Just as the views of the school philosophy on space and time make
it more difficult to understand the relativity theory, so its conception of
causality is an obstacle to an understanding of the new quantum
mechanics. I will not go into greater detail here concerning the causality
problem; I wish to draw attention to only one point.

Classical physics understood by the law of causality the calculahility
of future states from an initial state: if the state of the world or of an
isolated system is known exactly at one instant of time, then it is known
also for all future time. It was regarded as indubitable that with the
help of prescribable methods of measurement one could determine the
values of the quantities defining the state of a system— if not exactly,
then at least approximately. It was assumed that with increasing re-
finement of the methods of measurement it would be possible to in-
crease the accuracy arbitrarily. Hence, in principle, to such quantities
as lengths or field intensities, determining the state, were ascribed exact
numerical values.

That people held this conviction so firmly is owing to the belief of
the school philosophy that exact values of lengths or field intensities
must exist even if they are not yet known accurately to the person per-
forming the measurements. They are hidden in the nutshell referred to
by Bergson, and one must break through it to reach the true values.

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modern science and its philosophy

( It is quite natural that we cannot measure the exact length of a
rod. If I wish to assert, however, that through refinement of the
methods of measurement we can gradually come closer and closer
to the exact value of the length, it is first necessary to ask whether we
can define what we understand by exact length. For here we often
go in a circle. We define as exact value the limiting value approached
by the measurements as the method is increasingly defined. In this
definition we assume that such a limiting value exists. Its existence can
be shown empirically, if at all, only to within an uncertainty of a
definite order of magnitude. But in this way we have come no nearer
settling the question of the existence of an exact value.

According to the atomistic theory, the length of a rod is nothing but
the distance between two atoms. Since an atom is a system of electrons,
every such distance can be reduced to a distance between electrons.
Every measurement consists in a comparison of the measured body
with a measuring rod. But the latter is itself a system of electrons.
Hence every measurement of length ultimately leads to the substantia-
tion of a coincidence between electrons. By this, of course, is not meant
a coincidence in the literal sense, but something like the phenomenon
whereby one electron covers the other when viewed from a definite
direction. It does mean, however, that the measurement of length is
reduced to the observation of light diffracted or scattered by the two
electrons. Now it is clear that differences in length that are small in
comparison to the wavelength of the light involved can play no role
in this observation. Such differences cannot be observed through any
experiment of this sort, hence cannot be regarded as conceivable ex-
perience. The possibility of being able to refine arbitrarily the measure-
ment of length by refining the measuring technique can only be based
on the hope of being able to produce radiation of arbitrarily small
wavelength. The production of such radiation, which must therefore
have arbitrarily high frequency, is not very probable, however, ac-
cording to the observations that led to the formulation of the quantum
hypothesis. For then there must be light quanta of arbitrarily high
energy and exerting arbitrarily great forces on collision. Moreover,
there is another circumstance, first pointed out by Heisenberg, that

twentieth-century physics and school philosophy

makes impossible an exact measurement even to within the order of
magnitude of tlie errors that correspond to still attainable wave-
lengths. If, specifically, one goes to very high frequencies, so that the
collision force of the light quantum becomes very great, it is not pos-
sible to establish the relative velocity— in our case, the state of rest
relative to each other— of the two electrons, for the impulse imparted by
the light quantum changes their state of motion in an uncontrollable
way; this is the phenomenon that accounts for the Compton effect.

Just as there is no method of measuring the length of a rod with
arbitrary accuracy, so too there is no method of measuring the in-
tensity of an electric field with arbitrary accuracy. Every such measure-
ment is based on the observation of the force exerted on a test body
in the field. The charge and size of this body are assumed to be so
small that they do not disturb the field. This assumption, however,
contradicts the atomistic hypothesis, which has no cognizance of arbi-
trarily small and arbitrarily weakly charged test bodies. Therefore
the assumption that a field intensity is measurable with arbitrary ac-
curacy in principle is not justified.

The physicist who starts from the conceptions of school philosophy
must say to this argument that there really exist perfectly definite
values of lengths, but that nature is so constituted that it prevents us
from determining them. There are natural laws especially suited to this
purpose. This corresponds entirely to the conception of the relativity
theory according to which the absolute velocities of motion of aU
reference systems exist but the laws of nature are so insidious that they
prevent the observation of these velocities. The physicist who wishes to
represent this conception of the relativity theory which corresponds
to the school philosophy must assume the existence of realities to
which no concrete experience corresponds. So, too, the physicist who
assumes the existence of exact lengths of bodies must understand by
the word “existence” something that no longer has any connection
with the empirical sense of this word, which refers to something ex-
perienced or, at least, experiencible.

On the basis of this conception, the problem is then put: Is the
law of causality valid or not valid in nature? That is, do the initial

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modern science and its philosophy

positions and velocities of electrons determine these quantities for all
future time? Even if there were equations for wliich that were the
case, nothing at all is said about real experiences. For we know that
we cannot assign positions and velocities of electrons unequivocally to
our experiences even by successive approximations. That the law of
causality is not valid for our experiences involving the positions and
velocities of electrons has been made plausible by the experiments on
the diffraction of electrons as they are usually interpreted. If, to wit,
electrons fall on a grating, the direction in which a single one is de-
flected cannot be predicted from its initial position and velocity.

It is often concluded that electrons follow absolute chance in their
choice of direction, or even, as one occasionally finds it put in popular
presentations, that an irrational element plays a role, a kind of per-
sonification of the electron. This follows, however, only if one starts
from the picture given by school philosophy, according to which every
electron has a definite position and velocity, which nevertheless do not
determine its future.

From the standpoint of a purely scientific conception, on the other
hand, one will say that there are no individual experiences involving
positions and velocities of electrons from which the future of the latter
can be predicted unequivocally. Instead, it appears that the probability
that an electron will be deflected in a definite direction can be pre-
dicted from the experience of the initial experimental arrangement.
For these probabilities (the squares of the absolute values of the wave
functions ) Schrodinger, in his wave mechanics, sets up rigorous causal
laws. To the probabilities that occur in these laws and define the
state of the system one can therefore assign definite experiences. This
theory is called statistical. The statistical element here consists in the
maimer of assignment of experiences to symbols. Thus to certain
symbols, the squares of the absolute values of the wave functions, there
are assigned, not individual experiences, but numbers which are ob-
tained by averaging from a great many iiidividual experiences.

The task of physics is only to find symbols among which there exist
rigorously valid relations, and which can be assigned uniquely to our
experiences. This correspondence between experiences and symbols

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twentieth-century physics and school philosophy

may be more or less detailed. If the symbols conform to the ex-
periences in a very detailed manner we speak of causal laws; if the
correspondence is of a broader sort we call the laws statistical. I do not
believe that a more exact analysis will establish a definite distinction
here. We know today that with the help of positions and velocities we
cannot set up any causal laws for single electrons. This does not ex-
clude the possibility, however, that we shall perhaps some day find a
set of quantities with the help of which it will be possible to describe
the behavior of these particles in greater detail than by means of the
wave function, the probabilities. When we determine a number
through a so-called single observation, we really observe even in this
case only a mean value; "point experiences” are never recorded. The
assignment of symbols to experiences always contains then, strictly
speaking, a statistical or, if we like, a collective element. Thus it is
always a matter of making the assignment so as to go into detail to a
greater or lesser degree.

There can therefore never be the question— which the physicist
who is infiuenced by the school philosophy often thinks must be
asked— “Does strict causality hold in nature?” but rather, “What is the
character of the correspondence between our experiences and the
quantities describing the state of a system, which are subject to
rigorous laws?”

We see here, just as in the conception of the relativity theory, that
the physicist, if he consciously or unconsciously maintains the stand-
point of the school philosophy, is prevented from seeing the present
physical theories as assertions about real physical experiences. He is
easily led to find in them a mysterious, destructive element, raising
philosophical difficulties. He may even find in them a contradiction
to common sense.

If we investigate more closely the nature of the epistemology of
classical physics and its connection with school philosophy, we find the
following:

The general view was that, in the great system of symbols of which
the physical theories are composed, there exists a framework which,
with our experimental progress, must be gradually filled in. It appeared

119

modern science and its philosophy

to be definitely established that all phenomena can be reduced to the
motion of material points or the vibrations of a medium; that these
material points at every instant possess definite positions and velocities
by which all future states are unequivocally determined; that there are
timpi variables with the help of which all phenomena can be most
simply represented; and so on. It was believed that while it would be
necessary to make many changes during the filling in of the framework,
none would be made in the fundamental rods of the framework.

Through the relativity theory and quantum mechanics this con-
viction has been shaken. We know that even in those parts of the
symbol system that form the framework, much has had to be changed
and still more will have to be. We are in general no longer convinced,
as we were formerly, that the parts of the symbol system forming the
frame are already approaching a definitive form. This does not imply
the acceptance of any skeptical standpoint, but only the rejection of *
any distinction between the various portions of the symbol system.

Every physicist is convinced that with experimental progress, with
progressive refinement of the measuring technique, we will admit finer
and finer structures and will always have to introduce new variables
to describe the state of a system. Similarly, he must be convinced that
there does not exist for all eternity a rigid framework which is char-
acterized by the trio of space, time, and causality, and in which no ex-
perience can change anything. He must be convinced rather that for
these most general rules of assignment exactly the same must hold as
for the more special rules, the dependence of which on the progress
of human experience is not doubted.

Classical physics led to the opinion that this framework was, in its
essentials, completed. Hence it could be proclaimed by the school
philosophy as eternal truth. Our modem theoretical physics, which
admits progress in all parts of the symbol system, is skeptical only
when viewed from the standpoint of the school phUosophy. From the
standpoint of the purely scientific conception, which takes only ex-
periences for granted and looks upon the symbol system constmcted
for them as a means or an instrument, there is nothing skeptical in it.
Would it show skepticism if we asserted that the ultimate machine for

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twentieth-century physics and schooi philosophy

traveling through space does not have to resemble the present airplane,
not even in its most important parts; that it must have in common with
the latter only one thing, the ability to fly?

And now let us return to the question put at the beginning of this
paper: What is the significance of the physical theories of the present
day for the general theory of knowledge? From the standpoint of the
school philosophy they signify a disintegration of rational thought;
hence they are only rules for representing the results of experiments
and not cognitions of reality, which are reserved for other methods. For
those, however, who do not recognize these nonscientific methods, the
present physical theories strengthen the conviction that even in ques-
tions such as those concerning space, time, and causality, there is
scientific progress, along with the progress in our observations; that it
is therefore not necessary beside the thriving tree of science to assume
a sterile region in which reside the eternally insoluble problems in the
attempted solution of which men have been only rotating about dieir
own axes for centuries. There are no boundaries between science and
philosophy, if one only formulates the task of physics in accordance
with the doctrines of Ernst Mach, using the words of Carnap:

To order the perceptions systematically and from present perceptions to
draw conclusions about perceptions to be expected.

121

CHAPTER

is there a trend today toward idealism in physics?

I T is generally recognized that modem exact science, the creation
of which in the age of Galileo and Newton led to the great ex-
pansion of our technical civilization, is distinguished from an-
cient and medieval science by the fact that the psychic, anthropo-
morphic elements are being eliminated more and more from science.
In place of the medieval doctrines of “the most perfect orbit,” “the
position appropriate to a body,” “the difference between celestial and
terrestrial bodies,” and the like, we now have the mathematically
formulable laws of Newton’s principles, in which only observ able ^nd
measurable quantities occur. tThere is no doubt that the/physics of
Galileo and Newton has created a gulf between body and mind
which did not exist in the anthropomorphic, animistic science of the
Middle Age^This separation of the two became unpleasant to those
who were interested in a science that would account for the behavior
not only of inanimate bodies, but of all bodies in nature, including the
human body. Thus arose the problem of explaining the mind on the
basis of mechanistic physics, a problem which many have discussed,
but without ever making any real advance, and which is actually only
an apparent problem. Its insolubility in this form, which was really
obvious to all, led many scholars to have a deep dislike for mech-
anistic physics and to derive a malicious pleasure from every dif-

122

,is there a trend toward Idealism in physics?

ficiilty that the latter encountered. R. Ruyer is quite right when he
says:

That, basically, many scholars are tortured by the burden of this
original sin, mechanistic physics, is strikingly shown by their reaction when-
ever the mechanistic or quantitative conception of physics appears to sufFer
a setback. The most philosophical minds, far from being disturbed by this
setback, hope every time to find in it an opportunity for introducing once
more the subjective. This was the case with the discovery of potential energy,
gravitation, and the degradation of energy, as well as chemical afiBnity.^

One need not be surprised, therefore, if the recent revolutions in
the field of theoretical physics, the creation of the relativity and
quantum theories, were received by the scholars whom Ruyer called
“the most philosophical minds” with the same feelings as the preced-
ing theoretical overtumings, such as the degradation of energy. Indeed,
today one can hardly open a periodical or book dealing with the de-
velopment of our general scientific ideas without meeting such ex-
pressions as "the end of the age of Galileo,” “the failure of mechanistic
physics,” “the end of the hostility of science toward the spirit,” “the
reconciliation between religion and science.” There is even a book on
modern physics, by Bernhard Bavink, entitled “Natural Science on the
Path to Religion.” *

Some are of the opinion that the new physical theories of the
twentieth century have brought about a change in the general con-
ception of the world as important as that caused by0he physics of
Galileo, which replaced the animistic conception of the Middle Ages
by the mechanistic one of modem times. In the same way, the new
physics is supposed to form a bridge from the “mechanistic world con-
ception” of the eighteenth and nineteenth centuries to the “mathe-
matical conception” of the twentieth century. The latter is thought to
be nearer, in a certain sense, to the medieval, animistic conception
than to the mechanistic one, because in mathematics there resides an
“ideal” or “spiritual” element, and a “mathematical world” is not as

^R. Buyer, Revue de Synthdse 6, 187 (1933).

* B. Bavink, Die Naturwissenschaft auf dem Wege zur Religion (Frankfurt am
Main: M. Diesterweg, 1933).

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modern science and its philosophy

foreign to the spirit as is a mechanical world. This view was pre-
sented in all solemnity by General Smuts in his opening address at the
celebration of the centenary of the British Association of Science on
September 23, 1931.“ He said, among other things:

There is the machine or mechanistic world view dominant since the
time of Galileo and Mewton, and now, since the coming of Einstein, being
replaced by the mathematician’s conception of the universe ... If matter
is essentially immaterial structure or organization, it cannot fundamentally
be so di£Eerent from organism or life ... or from mind, which is an active
organize^

First, we must ask from the standpoint of the logic of science
whether the physical theories of the twentieth century really contain
any spiritualistic elements and, second, we must ask with what processes
outside of physics the demand for a spiritualistic conception of nature
is generally found to be associated. Let us begin by touching briefly on
the second question in order to be able to consider the first in greater
detail.

It is certainly no accident that the culmination of the mechanistic
conception of nature, as it is found, say, in the work of Laplace,
coincided with the triumph of the French Revolution. It is certainly
no accident that since that time the struggle against the “ideas of
1789” has almost always coincided with a criticism of this conception
of nature, a longing for a more idealistic or spiritualistic theory. The
struggle against the “ideas of 1789” has been crowned in recent years
by the fact that in a series of countries, especially in Italy and Ger-
many, a directly opposite world conception has prevailed politically.
This conception has a philosophic basis that is in sharp contradiction
to the mechanistic conception of nature and urges a more “organismic”
picture of the world, by which is meant a partial return to the spiritual-
istic or animistic doctrines of the Middle Ages, just as the new con-
ception of a state is connected with that of the Middle Ages. The ad-
herents of this antimechanistic, organismic conception of nature strive
to show that in the exact sciences “spontaneously,” “from purely
scientific considerations,” a revolution has taken place. According to

^Nature 128. 521 (1931).

}

,is there a trend toward idealism in physics?

^eir argument, on the basis of the relativity theory and quantum
mechanics one can set up a conception of nature in which the mind
again plays a role, and which is compatible with an “antimechanical,
organismic, independent” biology^

As a typical example, a work of B. Bavink may be quoted. Bavink
has a thorough knowledge of physics and biology and is an outstanding
representative of the “organismic conception of nature.” He maintains
that

today there reigns within the circle of the sciences a willingness to tie once
more the threads of science to all the higher values of human life, to Cod
and the soul, freedom of will, etc.— threads that seemed almost completely
severed; it is a willingness the like of which has not been present for cen-
turies. That this change should take place at the present time is a coincidence
almost hordering on the miraculous, for this change has in itself nothing to
do with pohtical and social transformations; it manifestly arose from purely
scientific motives.^

Whether or not the last sentence is correct is exactly the question we
are trying to answer.

On the other hand, in Russia, since the founding of the Soviet
Union, a system has been established that seeks its philosophic basis
in the "dialectical materialism” of Karl Marx as adapted by Lenin. I
do not wish here to discuss the relation between this “dialectical ma-
terialism” and what one is accustomed to call “materialism” in Germany
and France. I want only to call attention to the fact that in countless
articles in the philosophical and political journals of present-day Russia,
the tendency toward spiritualism which is often found as an accompani-
ment of modem physical theories is interpreted as one of the “phe-
nomena of decadence” of science in capitalist countries.' In these
articles the following line of thought oRen appears: in western
Europe science, to be sure, is still making progress on individual prob-
lems, such as the formulation of laws of atomic processes, just ias

*B. Bavink, “The Sciences in the Third Reich" (in German), Unsere Welt
25, 225 (1933).

' As a recent example may be cited A. K. Timiriazew, “The Wave of Idealism
in Modem Physics in the West and in Our Country” (in Russian), Pod znamenem
marksizma, 1933, no. 5.

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modern science and its philosophy ^

capitalist economy is still progressing technically. However, just as the
life of the industrial population is shaken more and more by crises
which finally make a generally acceptable solution impossible, so
science, in spite of its progress in details, cannot produce a satisfying
general picture of the processes in nature. In working on such a gen-
eral picture it no longer proceeds scientifically, in the modem sense.
Rather, it borrows from the animistic, spiritualistic physics of the
Middle Ages and interprets modem theories in this light, because the
intellectual trends dominant in political life obscure the scientific
theories by wrapping them in a spiritualistic fog.

In spite of the tremendous conflict between the “materialistic”
Soviet Union and the states based on the organismic conception of the
world, they all agree on the fact that the tendency toward spiritualism
in modem physics corresponds to the ideology of the new organismic
state. By some this tendency is welcomed as a necessary consequence
of modem physics; by others it is condemned as an adulteration of
it. That the representatives of both groups comprehend physics in this
way is a fact that is as well established empirically as the best observa-
tions of experimental physics, a fact which we must therefore take into
account in any consideration of modem physical theories.

I wish to say at once that the result of our investigation will be as
follows: In the process of eliminating the “animistic” nothing has been
changed in the slightest by the modern physical theories. This process
continues irresistibly forward as before. He who would interpret
physics by means of “psychic factors” had at the time of the physics
of Galileo and Newton the same justification as today. The role of the
“psychic” has remained exactly the same. Hence, if there does exist
today a greater tendency toward spiritualistic interpretation, it is con-
nected only with processes that have nothing at all to do with the
progress of physics.

Cjhe arguments that are supposed to show that psychic factors play
a greater role in modem physics than in the physics of Newton are of
various kinds. In one group it is claimed that the role of the “observing
subject” in the relativity and quantum theories can no longer be
eliminated from physical statements, as was still the case in “classical

126

is there a trend toward idealism in physics?

physics^jjfrhis argument is often put as follows: Whereas in classical
physics expressions like “length of a rod” or “time interval between two
events” assert something about “objective” facts, in the Einstein
relativity theory such expressions have a meaning only if the observer
to whom they refer is specified. One can only say, for instance, “This
body has a length of one meter with respect to this particular observer.”
It appears, therefore, that every physical statement possesses a psycho-
logical constituent. In popular literature on the relativity theory writers
often even go so far as to compare the various lengths of a rod for
various observers with the optical illusion that arises when one draws
two straight lines of equal length but places different ornaments at
their ends, producing the illusion of different lengths.

< > > <

^This conception,^ in its "scientific” as well as its “popular” form, is
based on^a complete misunderstanding' of the relativity theory^Vhere-
^ever in the theory of relativity reference is made to an observer, a
physical measuring instrument can be substituted. It is asserted only
that the results of the measurement will be different according as the
motion of the measuring instrument is different. But in this there is
nothing psychological,Jat any rate not any more than in classical
physics. The role of the observer is in both cases exactly the same: he
merely substantiates the fact that in a certain instrument a pointer
coincides with a division mark on a scale. For this purpose the state of
motion of the observer himself is quite immaterial. In the theory of
relativity, as well as in classical physics, it is assumed that such a sub-
stantiation is£ob]ective,” that there can never arise any difference of
opinion in connection with it. Naturally, it remains “subjective” in
the sense that some observer is necessary for it. Here “objective” means
“the same for all subjects,” or “intersubjective.’^

Similar considerations have also been associated with the quantum
theory. According to this theory, as Heisenberg showed, the position
and the velocity of a given particle can never be exactly determined
simultaneously. If one makes use of an experimental arrangement that

127

modern science and its philosophy

allows the position to be measured very accurately, the exacqfeeasure-
ment of velocity by means of the same experimental arrangement is
impossible. It is then held that whereas in classical physics a statement
about the position and velocity of a particle was a statement about an
objective fact, without any psychologic elements, in the quantum
theory one cannot speak of the position and velocity of a particle, but
only of what is given by a certain measurement. Thus every statement
about particles involves the observer himself, and hence contains a
psychologic element. To this argument we must reply as I have just
indicated in the discussion of the relativity theory, pointing out that
in quantum mechanics, too, what matters is never the observer, but
only the instruments of observation. The role of the human being as
observer is limited here again to establishing whether or not a pointer
on a scale coincides with a division mark. This observation, however,
is regarded here, just as in classical physics, as something “objective,”
or better, as something “intersubjective.” What one can learn from the
relativity and quantum theories in this connection is only what is also
given by a consistent presentation of classical physics: every physical
principle is, in the final analysis, a summary of statements concerning
observations, or, if one wishes to speak in a particularly physical way,
concerning pointer readings.

We have thus seen that the new role of “observer” in physics
cannot be used in favor of a tendency toward a more spiritualistic
conception of physics. There exists, however, a whole series of other
arguments which are customarily used to establish the approach or
“return” of physics to the “organic, idealistic” conception of nature.
Such arguments run somewhat like this; “Quantum mechanics con-
tains a teleological element,” or “The indeterministic interpretation of
the quantum theory makes room for free will.” Here we shall not con-
sider these questions, but shall speak of a still more general argument
for the “spiritualistic character” of modem physics. This is an argu-
ment which in recent years has been repeated so often and by scholars
of such prominence that there is danger that many, through becoming
accustomed to such lines of thought, will accept them as justified—
indeed, as obvious. These ideas have perhaps received the most

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>is there a trend toward idealism in physics?

extensive dissemination in 150,000 copies of a book by the outstanding
physicist and astrophysicist, }. H. Jeans. Jeans depicts the present
situation in physics as follows:

Today there is a wide measure of agreement, which on the physical side
of science approaches almost to unanimity, that the stream of knowledge is
heading towards a nonmechanical reality; the universe begins to look more
like a great thought than like a great machine. Mind no longer appears as an
accidental intruder into the realm of matter.®

Jeans bases his opinion that nature is to be regarded as something
“spiritual” essentially on the assertion that modem physics has shown
that one cannot give any mechanical representation of natural proc-
esses, although one can give a mathematical representation. He says:

The efforts of our nearer ancestors to interpret nature on engineering
lines proved equally inadequate . . . On the other hand, our efforts to in-
terpret nature in terms of the concepts of pure mathematics have, so far,
proved brilliantly successful.’

In the laws of mathematics, in contrast to those of mechanics, of
machinery, Jeans sees, however, a spiritual element. If nature behaves
according to mathematical laws, it must be the work of a mind which
can create mathematics, like the human mind, but is more compre-
hensive. Jeans is so strongly convinced that the movement toward
idealism is connected with the present state of theoretical physics that
he keeps in view the possibility that, with a change of the theories of
physics, there may again develop a movement away from idealism.
Thus he says in a later book:

So far the pendulum shows no signs of swinging back, and the law and
order which we find in the universe are most easily described— and also, I
think, most easily explained— in the language of idealism. Thus, subject to
the reservations already mentioned, we may say that present-day science is
favorable to idealism . . Yet who shall say what we may find awaiting us
roimd the next comer? ®

®J. H. Jeans, The Mysterious Universe (Cambridge: The University Press,
1930), p. 158.

Ubid., p. 143.

*J. H. Jeans, The New Background of Science (Cambridge: The University
Press, 1933), p. 296.

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modern science and its philosophy

Similar views are presented by Sir Arthur Stanley Eddington, in
his book The Nature of the Physical World." While there is in this
book a great deal that is beneficial in furthering the understanding of
modem physics and in bringing its results to a wide circle of readers
through a concrete and lucid presentation, yet it has numerous sections
which Eddington himself regards as bold interpretation of present-day
physics to which many will perhaps take exception, and which, in my
opinion, form obstacles to the task of fitting physics into a self-
consistent picture of the processes of the whole of nature. Eddington,
like Jeans, believes that these views are matters of faith and that it is
impossible to force one by proof to accept them. Thai is certainly tme.
However, what can be shown clearly, in my opinion, is that these
idealistic views have nothing at all to do with modem physics. If
anyone wanted to accept them, he could have done so just as well
in connection with the physics of Galileo and Newton, which is not
less "mathematical” than twentieth-century physics.

The arguments of both Jeans and Eddington depend on the con-
trast between a physics that reduces everything to mechanics (that
of Galileo and Newton) and one that bases everything on mathe-
matical formulas (the physics of Einstein and the quantum theory).
How can one formulate clearly the distinction between a “mechanical”
and a “mathematical” basis for the processes of nature? Newtonian
physics reduces all phenomena to the equations of motion for mass
points between which there act central forces, that is, to a system of
differential equations. The mechanics of Einstein changes these dif-
ferential equations in a few respects which give essential differences
only for very high velocities, and points out that the equations so
changed have mathematically the same form as the geodesics in a
curved (non-Euclidean, Riemannian) space. In place of one system of
differential equations, another occurs. Why then is one theory called
“mathematical,” the other “mechanistic”? Surely similarity to the
geodesics cannot be the only reason, for Newtonian physics can also
be brought into this form without any difficulty.

Adhering to the concrete interpretation of physics as a representa-

• Cambridge: The University Press, 1928.

130

is there a trend toward Idealism in physics?

tion of observable facts, we can try to summarize the difference be-
tween “mechanical" and “nonmechanical, mathematical” physics ap-
proximately as follows: By means of Newtonian mechanics we can
describe the motions of bodies with which we deal in everyday life,
so long as they have also the velocities that are encountered in daily
experience. To this class of bodies belong the ordinary tools such as
hammers and tongs, but also such things as steam engines, automobiles,
and airplanes. During the reign of the physics of Galileo and Newton
it was believed that in time it would be possible by means of these
same equations to describe also the motions of the smallest particles of
matter, such as atoms and ions, as well as the motions of celestial
bodies during arbitrarily long time intervals and with arbitrarily high
velocities. In other words, it was believed that all processes of nature,
in the large and in the small, could be covered by the same laws that
had been established for the motions of “bodies of average size with
moderate velocities.” This belief has been shaken by the development
of physics in the twentieth century. We know today that the motions
of bodies with velocities comparable to that of light can be described
only with the help of the relativity theory of Einstein, the motions of
the smallest particles in the atoms only with the help of quantum and
wave mechanics.

If we understand by mechanics the doctrine of the motion of
“bodies of average size with moderate velocities,” then we can rightly
say that modem physics has established the impossibility of a mechani-
cal basis for the processes of nature. If we say, however, that the
mechanical foundation has been replaced by a mathematical one, it is,
in my opinion, a very inappropriate mode of expression. We ought to
say, rather, that the place of a special mathematical theory, that of
Newton, has been taken by more general theories, the relativity and
quantum theories. The opinion that a special mathematical theory
could represent all the processes of nature has turned out to be false;
that is all. But from this fact no contrast between the propositions
“Newtonian physics = mechanics = materialism,” on the one hand, and
“modem physics = mathematics = idealism,” on the other hand, can be
deduced. .

131

modern science and its philosophy

Newton, in his Mathematical Principles of Natural Philosophy,^"
replaced the matter filling the world and acting tlirough pressure, col-
lisions, and fiuid vortices, as pictured by the Cartesians, by small
masses, almost lost in vast empty space and acting on each other only
through forces at a distance. When this work was published, the new
theory was hailed by many of his followers as a triumph over the
materialism of the "Epicureans.”

As proof, one need only read the famous controversy between
Leibniz and Clarke,*^ in which Clarke defends Newton's teachings
against the attacks of Leibniz. Clarke says in his first reply:

Next to the corruptible dispositions of human beings, it [the disavowal
of religion] is to be ascribed first of all to the false philosophy of the ma-
terialists, who oppose the mathematical principles of philosophy [i.e.,
Newton’s] . . . These principles, and indeed only they, show matter and
the body as the smallest and most insignificant part of the universe.

Hence at that time Newton’s followers, in so far as they were
adherents of spiritualistic metaphysics, extolled his teachings as “mathe-
matical” and “spiritual” in contrast to materialism. Today those with
analogous philosophic inclinations say that Newtonian physics was
“materialistic,” but that Einstein has again brought in a “mathematical,”
“spiritual” element in place of the mechanical one.

We have already seen that the assertion that the laws of nature
are not “mechanical” but "mathematical” means only that the laws are
expressed not by means of the special mathematical formulas of
Newton, but by means of the more general formulas of the relativity
and quantum theories. When, however, we say, not that the formulas
used to describe nature are mathematical, but that the world is mathe-
matical, it is difficult to say what we mean. By mathematics, con-
sidered concretely, we can only understand a system of formulas or
propositions. With these formulas are to be correlated the observations

“I. Newton, Philosophiae Naturalis Principia Mathematica (1687), tr. by
A. Motte (1729), rev. by F. Cajori (University of California Press, 1934).

A Collection of Papers, which Passed between the Late Learned Mr. Leibnitz,
and Dr. [Samuel] Clarke, in the Years 1715 and 1716 . . . (London: J. Knapton,
1717).

132

5 there a trend toward idealism in physics?

that we make of the processes of nature, if the formulas are to repre-
sent physical theories. The processes themselves, however, do not
consist of these formulas. In an assertion such as “The world is basically
mathematics,” the word “is” can only be used in a mystic sense, as it
occurs perhaps in the sentence “This architecture or this music is pure
mathematics.”

In order to make his views clear, Jeans must speak of the world
architect; he represents him, not according to Newtonian physics as a
kind of engineer, but according to modem physics as a kind of mathe-
matician. Since engineers also produce their work according to mathe-
matical formulas, Jeans has to indicate the distinction between the
engineer and the world creator somewhat as follows: The engineer fits
his formulas to the observations, whereas the creator invents formulas
at will and then constructs the world according to them. Jeans brings
in here the difference between “pure” and “applied” madiematics. The
engineer is an applied mathematician, the world creator a pure one.
Jeans tries to show it in this way: The man who works in pure mathe-
matics invents formulas and propositions without any regard to the
question of practical application; later, it turns out that the physicist
or engineer, by means of the results obtained by the pure mathe-
matician, can represent the processes of nature, of which the pure
mathematician knew nothing when he devised his theory. This can only
be explained by saying that the processes are themselves the work of
a pure mathematician, and the theoretical physicist who finds these
formulas for representing observations is only rediscovering the ideas
of the pure mathematician who created the world. The creations of
the demiurge must accordingly agree to a large extent with those of a
human pure mathematician.

The assertion that the world is built according to the principles of
“pure” mathematics is to be found not only in the works of Jeans. It
is very often used in setting up mystical conceptions of the world. If
one wants to be clear as to its meaning, one must first of all obtain
clarity as to the meaning of the propositions of “pure” mathematics in
general. According to the conception of B. Russell and L. Wittgenstein,
which is also that of the Vienna Circle, the propositions of pure mathe-

modern science and its phiiosophy

matics are not statements concerning natural processes, but are purely
logical statements concerning the question of what assertions are equiv-
alent to one another, which can be transformed into one another by
formal transformations. The propositions of pure mathematics, there-
fore, remain correct, no matter what the natural processes may be; these
propositions can be neither confirmed nor refuted by observation, since
they state nothing concerning the real processes of nature. Mathemati-
cal theorems, as is often said, are of an analytic character.

For example, if I prove the theorem “The sum of the angles of a
triangle is equal to 180“” as a proposition of pure mathematics, I
prove only that from the axioms of Euclidean geometry, including the
axiom of parallels, it follows by logical transformation that the sum of
the angles of a triangle is equal to 180“ if the straight lines and points
of which it consists have all the properties ascribed to them by the
Euclidean axioms. That is to say, if for a concrete physical triangle 1
can establish by observation the validity of the Euclidean axioms, then
the sum of the angles is equal to 180“. In other words, the statements
"The sum of the angles is 180“” and "The axioms are valid” are only
two expressions of the same thing, two statements with the same con-
tent (where, of course, the proposition of the sum of the angles is
only a part of the content of the whole system of axioms). Once this
has become clear, the world, whatever it may be, will always obey the
propositions of pure mathematics; the assertion that it obeys them says
nothing at all about the real world. It says only what is self-evident,
that all statements about the world can be replaced by equivalent
statements.

Something else must obviously be meant, however, when Jeans and
so many others say that the world is constructed according to the
principles of “pure” mathematics. As an example, the following is ad-
duced: Mathematicians— ChristofFel, Helmholtz, Ricci, Levi CivitA, and
others— long ago built up the theory of the curvature properties of
Riemannian space. When Einstein set up his general theory of rela-
tivity, he found this whole branch of mathematics ready for him. Al-
though it was invented without any intention of its being used in

134

is there a trend toward idealism in physics?

physics, Einstein was able to apply it in his theory of gravitation and
general relativity. One must therefore assume that the creator built
the world according to those principles of pure mathematics. Other-
wise it would be an inconceivable coincidence that such a complicated
branch of mathematics, developed for quite other purposes, could be
used for the theory of gravitation.

We have already seen that this assertion cannot mean that the
^rld is built according to the propositions of the Riemannian cuirva-
ture theory or of the absolute difiFerential calculus invented by Ricci
and Levi Civiti; for these propositions, like the proposition of the
sum of the angles and all other propositions of pure mathematics, are
only statements of how one can express the same thing in different
ways. The assertion, therefore, can only mean that the concepts and
definitions of pure mathematics— the geometry of Riemannian spaces
—created certain structures— the Christoffel three-index symbols, the
Riemannian curvature tensor— which could be utilized in the Einstein
theory of gravitation. This, however, is the same, although perhaps
on a higher level, as saying: ‘The concepts of the square or the square
root or the logarithm have come out of pure mathematics; it is therefore
amazing that they also occur in the formulas of physics.” If we now use
the possibility of representing the world according to Einstein, with
the help of the Riemannian curvature tensors, as proof that the world
was created by a mathematician, we might have said with the same
justification, back in the time of Newton, that the world must have been
created by a mathematician; for in Newton’s formulas the cliief role
is played by the “square of the distance,” and the concept of the
square of a number originated in geometry and was introduced with-
out any regard for physics. If we consider the matter from this stand-
point, that is, if we speak not of mathematical theorems but of mathe-
matical concepts, a little reflection shows that the distinction drawn
by Jeans between engineer and mathematician, or between “applied”
and “pure” mathematics, cannot be maintained.

As a matter of fact, concepts such as those of Riemannian curvature
have always been invented for the purpose of representing some prob-

135

modern science and its philosophy

lem of concrete reality, for describing processes of nature. The con-
cepts of Riemannian geometry all go back to the problem of describing
the motion of a real rigid body in general coordinates; one need only
recall the work of Helmholtz on the facts at the basis of geometry
Riemann, Christoffel, and Helmholtz set up certain mathematical ex-
pressions which are equal to zero in the case of the motion of a rigid
body, according to the usual laws of physics. When Einstein proceeded
to formulate the deviations from these laws, it was clear that he had
to begin with the expressions that gave the properties of rigid bodies,
according to classical physics, in a form valid for all coordinate sys-
tems. If there existed any deviations expressible independently of the
coordinate system, it had to be possible to express them so that the
quantities which in the old physics had the value zero were now dif-
ferent from zero and took on values depending in a simple manner
on the distribution of matter. If such a simple dependence did not exist,
then there could exist no laws independent of the coordinate system, as
Einstein required. If such laws did exist, it had to be possible to ex-
press them through the concepts that were at hand for representing
the motion of a rigid body. But this gives no evidence that the world '
creator was a “pure mathematician.” The' only thing that must be re-
garded as a real and astonishing characteristic of nature is the fact that
there do exist, in general, simple laws for the description of nature.
This, however, has nothing to do with the distinction between “me-
chanical” and “mathematical.”

If today expressions with spiritualistic coloring are used to a greater
extent than in the nineteenth century, this has no connection with any
“crises in physics” or with any “new physical conception of nature.” It
is rather associated with a crisis in human society arising from quite
different processes. In opposition to the materialistic social theories
there have come into the foreground movements based on an “idealis-
tic” picture of the world. These movements seek support in an idealistic

“ “XJber den Urspning und die Bedeutung der geometrische Axiome” ( 1870),
translated as “On the Origin and Significance of Geometrical Axioms," in Helm-
holtz, Popular Lectures on Scientific Subjects, series 2, tr. by E. Atkinson (London:
Longmans, Green, 1881).

136

^ is there a trend toward idealism in physics?

or spiritualistic conception of nature. Just as at the end of the nine-
teenth century analogous movements made use of energetics, the
electromagnetic picture of matter, and so on, to prophesy the end of
“materialistic” physics, so today die relativity and quantum theories
are being used. All this, however, has no real connection with the prog-
ress of physics.

137

CHAPTER

mechanical "explanation” or mathematical description?

% A #HEN the physics of Galileo and Newton put an end to
\m\mche animistic period, it received the honorary title “mathe-
y Viatical.” At that time Newton wrote the Mathematical Prin-
ciples of Natural Philosophy. A pronounced antimaterialistic tend-
ency was ascribed to this work, because in it palpable impacts of
masses upon one another were replaced by a pure mathematical for-
mula, the law of attraction. The physics of Galileo and Newton did
not come to be called “mechanistic” until it had become customary
to use the treatment of mechanics as a model for every other field.

The Newtonian mechanics was looked upon more and more as the
standard type of a theory. Helmholtz, for example, said:

To understand a phenomenon means nothing else than to reduce it to
the Newtonian laws. Then the necessity of explanation has been satisfied in a
palpable way.

It was completely forgotten that in Newton’s own day his theory
was looked upon as a set of abstract mathematical formulas, which
needed a mechanical explanation to satisfy man’s desire for causality.
Newton himself recognized this need, but he declined to take part in
satisfying it himself, when he made the now well-known remark,
"Hypotheses non fingo.” But men like Huyghens and Leibniz never
considered the Newtonian theory a physical explanation; they looked

138

meohanical "explanation" or mathematical description?

upon it as only a mathematical formula. Thus even at the very begin-
ning of the development of mechanistic physics, it was not easy to de-
fine precisely the distinctions between a “mechanistic” and a “mathe-
matical” theory.

Much later a contradiction began to be noticed between “mathe-
matical” and “pictural,” ^ and it was asserted that only the reduction
to mechanics guaranteed a theory that provides a pictural representa-
tion and that without this pictural character no real understanding was
possible. It was claimed, for example, that Maxwell’s field equations of
electrodynamics are not pictural, if they are not illustrated with a
mechanical model.

There were two motives involved in the resistance to the abandon-
ment of mechanism. First, there was no inclination to renounce the
“explanatory” value that was ascribed to mechanistic theories only;
second, it was feared that the abandonment of mechanistic explana-
tions would lead to a return to medieval animistic anthropomorphic
science.

But in speaking of this desire for picturization we ought to be ,
clear as to the actual meaning of the term. The mechanical laws de-
scribe for us the ordinary experiences of daily life— the use of tools,
automobiles, firearms, as well as the movements of the planets. We find
it desirable to interpret all other experiences by analogy with those
that are most familiar.

The physics of the nineteenth century showed that this wish can-
not be fulfilled. Electromagnetic phenomena cannot be reduced to the
same mechanical laws that govern guns or tools. Nevertheless, the laws
concerning electromagnetic phenomena may be considered in a
broader sense as also pictural. We can verify experimentally the valid-
ity of such physical laws as, for example. Maxwell’s field equations if
we can derive from them a result that is directly observable experi-
mentally. The experiment consists in observing the position of the
pointer of an ammeter or of some other measuring apparatus, or the dis-

^We here translate the German word amchaulich by the English pictural,
which we take to imply, as the German does, both the ordinary visual perception
of objects and the mental visualization oC them. See also Chapter 7.

139

modern science and its philosophy

placement of some colored spot. But these are precisely the kind of
observation that we use to verify the laws of ordinary mechanics. In
the end only gross mechanical events, which certainly are pictural,
are derived from the equations of the electromagnetic field, and this
holds in all physics, including that of the twentieth century. In this
sense physical laws must be pictural if they are to have any scientific
meaning at all, for otherwise they are not experimentally verifiable.
The fundamental equations by themselves need not be pictural, since
they cannot be submitted to any direct experimental verification.

For a long time efforts were made to set up a mechanical explana-
tion of Maxwell’s theory. There was always the feeling that without it,
something essential to the understanding of electromagnetic phenom-
ena was missing. Heinrich Hertz finally cut the Gordian knot, so to
speak, when he said: “Maxwell’s theory is nothing else than Max-
well’s equations. That is, the question is not whether these equations
are pictural, that is, can be interpreted mechanistically, but only
whether pictural conclusions can be derived from them which can be
tested by means of gross mechanical experiments.”

These words gave birth to what we call today the “positivistic con-
ception” of physics. Positivistic physics thus replaced mechanistic
physics. The mechanistic explanation could now be abandoned as a
foimdation, without at the same time renouncing the achievements of
the epoch of Galileo and Newton. If a positivistic conception of physics
was accepted, the rejection of medieval animism was as complete as in
mechanistic physics. In place of the mechanical model there was the
mathematical formula with its experimentally verifiable results. In this
sense, it may be said that the positivistic conception replaced the
mechanistic interpretation with a mathematical one. Before anything
was known about the relativity or the quantum theories, before, there-
fore, even the “rebirth of idealistic physics in the twentieth century,”
Hertz, Mach, Duhem and others had already seen that the essential
point in every explanation of nature is not the mechanical model but
rather the construction of mathematical relations.

The historical error is often made of connecting the struggle of Mach
and Duhem for the positivistic physics with their aversion for atomism.

140

mechanical "explanation" or mathematical description?

so that a victory for atomism was considered a defeat for positivism.
In reality the champions of atomism, Maxwell and Boltzmann, were
exactly of the same opinion concerning the general nature of a physical
theory as Hertz and Mach. The difference in their views about the
value of atomistic theories arose only because they differed in their
estimates of the convenience with which the actually known physical
phenomena could be derived from these theories.

A few quotations from the writings of Maxwell and Boltzmann
win at once make clear what they thought concerning the structure of
physical theories and their connection with experience.

In the introduction to his treatise. On Faradays Lines of Force,
Maxwell expressed himself quite clearly on these questions. Boltzmann
says in the notes to his German translation of this paper:

Maxwell’s introduction proves that he was as much of a pioneer in the
theory of knowledge as he was in theoretical physics. All the new ground in
the theory of knowledge that was broken in the next forty years, is already
clearly marked out in these few pages; indeed the very ideas are illustrated.
Later epistemologists treated all this more fully, but also with greater bias.
They set up rules for the future development of a theory after it had
already developed and not before, as was the case with Maxwell.

Maxwell describes how he first found a convenient mathematical
formulation of the laws of electricity and magnetism that were already
known, and then used the mathematical concepts so created for the
construction of the new laws;

In order therefore to appreciate the requirements of the science, the
student must make himself familiar with a considerable body of most intricate
mathematics, the mere retention of which in the memory materially inter-
feres with further progress. The first process therefore in the effectual study
of the science, must be one of simplification and reduction of the results of
previous investigation to a form in which the mind can grasp them. The
results of this simplification may take the form of a purely mathematical
formula or of a physical hypothesis.^

® J. C. Maxwell, “On Faraday’s Lines of Force,” Transactions of the Cambridge
Philosophical Society 10, part 1 (1855); Scientific Papers of James Clerk Maxwell
(Cambridge University I^s, 1890), vol. 1, p. 155.

141

modern science and its philosophy

■ But Maxwell by no means tliinks that there is an essential antithesis
between a “purely mathematical formula” and a “physical hypothesis.”
He judges them only according to their practical exchange value, and
finds that each of them has its advantages and disadvantages. Hence
he looks for a kind of theory that is more general than either and that
combines the advantages of both without the disadvantages. This more
general sort of theory Maxwell finds in the physical analogy. It com-
prehends both the physical hypothesis, in which an analogy is drawn
between electromagnetic events and a mechanical model, and a mathe-
matical formula, which points out an analogy between the phenomena
of electricity and certain mathematical relationships that are given
by the electromagnetic-field equations.

Maxwell continues:

In the first case [of a purely mathematical formula] we entirely lose sight
of the phenomena to be explained; and though we may trace out the conse-
quences of given laws, we can never obtain more extended views of the con-
nections of the subject. If, on the other hand, we adopt a physical hypothesis,
we see the phenomena only through a medium, and are liable to that blind-
ness to facts and rashness in assumption which a partial explanation en-
courages ... In order to obtain physical ideas without adopting a physical
theory we must make ourselves familiar with the existence of physical
analogies. By a physical analogy I mean that partial similarity between the
laws of one science and those of another which makes each of them illus-
trate the other. Thus all the mathematical sciences are founded on relations
between physical laws and laws of numbers, so that the aim of exact science
is to reduce the problems of nature to the determination of quantities by
operations with numbers. Passing from the most universal of all analogies to
a very partial one, we find the same resemblance in the mathematical form
between two different phenomena giving rise to a physical theory of light.®

In the introduction to his lectures on the theory of gases Boltzmann’s
view is brought out very clearly. In one place he says:

The question as to the fitness of the atomistic philosophy is naturally
wholly untouched by the fact stressed by Kirchhoff that our dieories about
nature bear the same relation to it as symbols to the things symbolized, as
letters to sounds or as musical notes to tones, and by the question whether

®Iiid.,pp. 155 f.

142

me^anical "explanation" or mathematical description?

it may not be expedient to consider our theories as pure descriptions so
that we may always recall their relation to nature. Therefore the question is
whether the pure differential equations or atomism will one day turn out
the more complete descriptions of phenomena.^

^L. Boltzmann, Vorlesungen iiber Castheorie (Leipzig; Barth, ed. 3, 1923),
vol. 1, p. 6.

143

CHAPTER

modern physics and common sense

A LMOST every new physical theory has to face the commonplace
accusation that it stands in contradiction to everyday experi-
# \ ence or, as it is sometimes put, that it contradicts common sense.

The heliocentric system of Copernicus is perhaps the most famous
example of a theory that has been charged with being in contra-
diction to the evidence of our senses. For on the one hand, many of
us have grown accustomed to believing that our eyes disclose to us the
earth is at rest with the sun and planets revolving around it. On the
other hand, the Copemican theory, established since the time of Galileo,
maintains that the sun is at rest and the earth revolves around it, "in
contradiction to this immediate testimony of our eyes.”

Although this accusation has been made in innumerable books, ar-
ticles, and lectures, it is difficult to understand what could be meant
by a physical theory’s being in contradiction to the evidence of our
senses. Such a contradiction could occur only if the theory implied
propositions about directly observable matters which were not con-
firmed by actual observations. This, however, is not the case for the
Copemican theory. In point of fact, the content of our observations
on sunsets and sunrises can be deduced from the heliocentric theory
as well as from the geocentric one. It must therefore be noted that
our sensory observations are not adequately formulated in such a
proposition as “We see immediately that it is the sun which is moving

144

modern physics and common sense

and not the earth.” For when we formulate our direct observations of
die solar motions we obtain statements like the following: “The
distance between the sun and the horizon increases from morning to
noon, and decreases from noon to evening.” And such propositions
can obviously be deduced from the Copemican as well as from the
Ptolemaic theory. Consequendy, the charge of a contradiction between
a given physical theory and the evidence of our senses cannot be sup-
ported, if we understand by “evidence of our senses” the propositions
that can be deduced from the theory and checked by experiment.

Our preference for the heliocentric theory rather than the geo-
centric one is based on the following two points. First, the heliocentric
theory makes it possible to calculate more simply the observable posi-
tions of the planets in their orbits than does the geocentric theory.
Second, generalizations, such as Newton’s laws of motion, can be made
much more easily on the basis of the heliocentric theory than on the
geocentric one. Such facts of observation as the perturbations of the
planetary orbits could be shown to be consistent with the geocentric
theory only by using formulas and computations that would exceed
the powers of a human mathematician. On the other hand, starting
from Newton’s laws of motion these perturbations can be calculated
with the help of relatively simple formulas within die framework of
the heliocentric theory.

So much for the logical issues involved in the charge. There is,
however, an obvious psychologic reason why people continue to
make it. If we consider only the facts of everyday experience, such as
the daily rising and setting of the sun, moon, and stars, we discover
that they can be deduced from the geocentric theory with great ease.
To deduce from this theory the facts concerned with the movements of
the planets is still possible, though highly inconvenient and involved.
If now we also consider the phenomena of perturbation, we find that
to deduce them from the geocentric theory is practically impossible,
and that the Copemican theory alone is capable of handling them. On
the other hand, the deduction of everyday phenomena like sunrise
and sunset can be performed more easily and simply from the geo-
centric theory than from the more “artificial” heliocentric theory— es-

145

modern science and its philosophy

pecially if we take the latter in its completely developed form as given
by Newton, so that it becomes adequate for encompassing the phe-
nomena of planetary perturbation.

We may therefore formulate the difference in function of the two
theories in the logical system of science as follows: If we are concerned
J with the deduction of phenomena occurring in the narrow domain of
everyday experience, it is convenient to use the geocentric theory. But
since the scope of the facts falling within the province of this theory is
very restricted, if we seek a theory that will embrace as many phe-
nomena as possible (including phenomena remote from daily experi-
ence), we must make use of the heliocentric theory.

Because the geocentric theory is more convenient for handling
familiar phenomena of daily life, it is often called an “intuitive” or
“visualizable” theory. Indeed, many people have the impression that
they fully understand this theory by a direct, immediate observation
of facts, and that no logical gap separates it from the content of our
naive sensory observations. However, all these characterizations of
the theory mean nothing more than that a relatively simple chain of
deductions connects it with the observable phenomena of daily life.

On the other hand, because the deduction of our most familiar
observations from the heliocentric theory is not as simple as in the
case of the geocentric one, there is a common impression that the
former is not connected closely with everyday experience. It has
therefore been called an “abstract” or “nonintuitive” theory, appar-
ently because the facts of experience upon which it rests occur only in
the context of scientific research, as when we use astronomical in-
struments to determine the exact positions of the stars.

This familiar distinction between “intuitive” and “abstract” theories
is, however, often misunderstood and misused. Thus, it has been said
that “intuitive” theories are the only sound ones, because they alone
serve as a stimulus to the physicists to carry on fruitful research. They
have also been said to offer a true representation of the real world in
terms of faithful pictures or images, thus furthering the scientist in his
search for the truth. On the other hand, "abstract” theories, which

146

, modern physics and common sense

employ mathematical formulas rather than the method of pictorial
representation, have been characterized as impediments to scientific
progress. It has been said of them that they can at best register knowl-
edge already achieved, but that they are of no help in the discovery of
new knowledge.

These alleged differences between intuitive and abstract theories
are regarded as particularly significant by followers of Kant and other
adherents of German idealistic philosophy. For intuitive or visualiz-
able theories have been claimed to be “anschaulich” in the sense
specified by Kant. Now in everyday German the word Anschauung
simply means the observation of an object, especially a visual obser-
vation, for example, the visual perception of a table. But for Kant and
other idealistic philosophers it frequently has a half-mystical meaning.
Thus, when they speak of an “innere Anschauung” or “internal intui-
tion” of the properties of a triangle, for example, they do not mean to
refer to a visual perception of a triangle, but to some mental act of
concentration upon the triangle, which itself exists only in the mind
as an image. We shall translate the term innere Anschauung by the Eng-
lish word “picturization,” and anschaulich by “pictural.” According to
the Kantian philosophy, we are supposed to be able to “see” directly
in this mental act such things as that the sum of the angles of a triangle
must be equal to two right angles. Accordingly, this alleged power of
picturization is claimed to be able to establish the essential properties of
triangles without appealing to empirical tests and without regarding the
theorems of geometry as propositions consisting of observation terms
—where “observation” is used in the familiar sense of observation
through the senses. In this way Euclidean geometry was “proved” to Jbe
the only legitimate geometry. The non-Euclidean geometries were al-
leged to have been demonstrated to be false, because their theorems
were not guaranteed by picturization. In opposition to these dicta, we
must note, however, that the propositions of non-Euclidean geometry
can be formulated in observational terms just as the Euclidean prop-
ositions can be, and that the alleged absurdity of the former arises
only from the fact that they are required to be “tested” by an internal
intuition.

-» •

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modern science and its philosophy

These ambiguities in the meaning of “intuition” or Anschauung
have made it possible for the intuitive theories of physics to acquire a
special importance in the eyes of philosophers and even of some physi-
cists. In the Germany of 1939, for example, the differences between
intuitive and abstract theories were linked up with differences between
races. Intuitive theories were associated with the characteristics of the
Nordic race, while the abstract ones were taken as expressing the pe-
culiarities of the Mediterranean races, especially of the Semites, though
sometimes even of the French. Naturally, since the Nordic race was re-
garded as the superior group, intuitive theories were also superior to
the abstract ones.

But the preceding discussion of the differences between the helio-
centric and the geocentric theories makes clear just what the difference
between these two types of theory really signifies. What is usually
called an "intuitive” or pictural theory is simply a theory very well
adapted to formulate in a simple and convenient manner our everyday
j experiences; an abstract theory, on the other hand, attempts to cover a
more inclusive domain of phenomena, and does not hesitate therefore
to formulate the familiar facts of daily life in a somewhat complex
marmer.

If we are once clear about the differences between the geocentric
and heliocentric theories, we are prepared to understand and evaluate
the objections often raised against more recent physical theories, such
as the theory of relativity or the quantum theory. These objections tend,
in the main, to allege that the new theories are too abstract and that
they use conceptions very far removed from those employed in every-
day experience. Indeed, some physicists have argued that the newer
conceptions are too remote from the notions employed by physicists
themselves in their laboratory researches.

Our previous analysis supplies us with a clue for evaluating these
objections. The laws formulated by so-called classical physics are
obtained from the study of material bodies and optical phenomena as
these occur either in everyday experience, or in physical experiments
carried on under conditions not very different from die circumstances

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modern physics and common sense

of everyday experience. With the help of these laws, the behavior of
bodies and of light in these domains can be expressed in a simple and
useful way. Until the end of the nineteenth century these laws have
been supposed to govern all the phenomena of the physical world,
from the smallest bodies, like electrons, to the largest ones, like suns
and stars, and from motions with low velocities to motions with the
velocity of light. But the development of physical research at the end
of the nineteenth century and the beginning of the twentieth showed
that the laws of classical physics are valid only for small velocities and
large bodies— to speak more exactly, for masses far greater than the
mass of an electron, and for velocities far less than the velocity of
light.

Now to express the behavior of things that do not occur in daily
experience, such as small particles with large velocities, we require a
generalization of classical physics and new types of physical law.
These new laws are naturally more complex than the laws of classical
physics, especially if we compare them in their applications to phe-
nomena of common experience; in these domains the laws of classical
physics are limiting cases of the new laws of relativity and quantum
physics. On the other hand, there is no sense in saying that these new
laws, when applied to phenomena, such as those within the hydrogen
atom that do not occur in daily experience, are more complex than the
classical laws, because the classical laws do not apply to these phe-
nomena at all. Consequently, only in the sense indicated is it correct
to say that the laws of classical physics are more closely related to
everyday experience than are the laws of twentieth-century physics,
namely, the laws of relativity and quantum physics.

It is evident, therefore, that from the standpoint of the logical
analysis of science the difference between intuitive and abstract theo-
ries is a very superficial one. That distinction does not play the im-
portant role in science that philosophers and laymen influenced by
orthodox philosophy suggest it does.

A glance at the history of science also reveals that the alleged wide
gap between these two kinds of theory is not understood in the same

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manner at every period of the history of science. Thus, at the time of
its discovery, Newton’s theory of motion was regarded as an abstract,
merely mathematical theory; in our own day, however, it is often cited
as an example of an intuitive theory, especially when philosophers wish
to establish the abstract character of the theory of relativity and of
quantum mechanics by contrasting them with an intuitive theory. In
truth, however, the alleged diflFerence between Newtonians and rela-
tivistic mechanics depends only on the undeniable fact that the difficult
and complicated calculations and deductions required for under-
standing Einstein’s theory of relativity are not required for under-
standing the phenomena of everyday experience. For these phenomena
can be formulated with the help of the more simple Newtonian theory
of mechanics. Hence the statement that a theory like Einstein’s is
abstract and nonintuitive simply means that it is more complex than
is necessary for a theory that need describe only the facts of daily
experience.

It is often maintained that whether a given scientist will be more
inclined to use an intuitive rather than an abstract theory is a function
of his personality. These psychologic factors are sometimes taken to
be facts of individual psychology, sometimes of race or of nationality.
It seems to me, however, that the importance of such psychologic
considerations has been exaggerated. Such psychologic factors seem
to play little role in the work of the great masters of science to whom
we are chiefly indebted for the present state of the sciences. Some
masters of science exhibit a “double personality.”

For example, the great English physicist J. Clerk Maxwell em-
ployed elaborate mechanical models in his work, as well as abstract
mathematical theories. He discovered many new facts with the help of
both types of theory, and was himself firmly convinced that there is no
fundamental difference between these two types from the point of view
of the logical analysis of science. Indeed, he emphasized the fact that
both abstract and intuitive theories are special cases of a more inclu-
sive type of formulation of physical facts, namely, formulation or
representation by analogies. And if we examine the work of Boltz-
maim and other great physicists interested in the logical structure of

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science, we find them regarding physical theories in the same charac-
teristic way.

"We may therefore sum up our considerations on the differences
between abstract theories and those alleged to be intuitive and com-
prehensible to common sense. Intuitive theories try to preserve so far
as possible the method of representation invented for handling
most simply the facts of daily life. Such theories are therefore com-
prehensible to everyone who is concerned with those facts and are thus
comprehensible to so-called common sense. Mechanical images or
models are particularly cherished in this context, and conservative
minds will perhaps always prefer theories using this method of repre-
sentation."

''But the progress of physical research reveals facts that cannot be
adequately covered by such intuitive theories. Progressive physicists
therefore try to find new ways of representation, new theories which
are adequate for as broad a domain of facts as possible, irrespective
of whether the new methods supply the simplest representation of the
facts that occur in everyday experience. It is thus possible that a new
theory, although the simplest one thus far invented for handling sub-
atomic phenomena, turns out to be quite complicated for representing
such phenomena as apples falling from trees. For this reason such a
theory is alleged to be incomprehensible to common sense, and con-
servative minds are always reluctant to accept it.

It is thus evident that the difference between the so-called two types
of theory has little to do with the psychologic difference between those
^physicists who like to reason abstractly and mathematically and those
who like to use concrete images or models. If we examine carefully the
work of modem physicists engaged in research on the quantum theory,
we discover that the psychologic fact that some of them prefer mathe-
matical formulas while others prefer geometric imagery does not ac-
count for their attitude to the quantum theory. For the majority of
physicists accept that theory, while only a minority denounce it, claim-
ing that their “mental constitution” forces them to regard quantum
theory as incomprehensible to common sense and as an unsuitable basis
for laboratory research. Indeed, representatives of both psychologic

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modern science and its phiiosophy

types are found among those physicists who have contributed to the
progress of quantum theory.

The common impression that there is a profound gap between these
two kinds of theory may perhaps be due to the fact that the funda-
mental propositions of science are often formulated in what Carnap
calls the “material idiom” instead of in the “formal idiom.” Thus, if we
ask whether the physical world consists of bodies situated in space
whose motions are governed by laws, or of purely mathematical prop-
erties of a four-dimensional space-time continuum, we have formulated
the question in the “material idiom” or “material mode.” So formulated,
it leads to innumerable disputes of a metaphysical character. We can
avoid such disputes by stating the question in a consistently scientific
form, using the “formal idiom.” When so stated it becomes the follow-
ing; Do the fundamental propositions of physics (i.e., its most general
laws) contain only terms of the thing-language, or do they contain also
terms that do not occur in the thing-language? ' It is important to ob-
serve that even if the second alternative should be the case, the terms
not occurring in the thing-language are reducible to terms in the thing-
language; for otherwise the propositions containing them would be
neither confirmable nor refutable in experience. It is clear, therefore,
that when the question has been stated in this way, the difference
between abstract and intuitive theories has ceased to have the funda-
mental character often attributed to it. For when the formal idiom is
used, the difference simply amounts to the difference between proposi-
tions containing only thing-terms and propositions containing other
than thing-terms which are, however, reducible to thing-terms.

Since it is just our everyday experiences that are most conveniently
formulated by the so-called intuitive theories, especially those using the
language of mechanical models, the outstanding characteristic of such
theories is that they give rise to the introduction of a thing-language.

^ The term “thing-language” is used by Camap in the description of the world
of our sense experience, as an alternative to “phenomenal” language. The latter
decomposes our impressions of the physical world into elementary sensations, such
as those of small areas of red or blue. The thing-language speaks of complexes of
sense impressions as they occur in our everyday language, like “table,” "chair,”
"man.”

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modern physics and common sense

And certainly an intellectual effort is required to overcome the reluc-
tance to using a language that is not a thing-language, however useful
such a new language might be for formulating the laws of physics about
facts discovered by recent research. Accordingly, we can extract one
grain of truth from the claim that intuitive theories (especially mechani-
cal ones) are the only genuine physical theories that are compatible
with the requirements of the laboratory scientist. This grain of truth lies
in the postulate that every physical theory must contain only such
terms as are reducible to terms of the thing-language. This postu-
late, stated in other words, simply means that every physical theory
must be tested in terms of propositions that deal with the facts of
everyday experience.

The theory of relativity has often been described as abstract, in
contrast with theories about the ether, which are said to be intuitive or
pictural. For the latter theories introduce a matter-like ether, which
is asserted to behave in many ways like the bodies of everyday experi-
ence, while relativity theory, on the other hand, introduces only ab-
stract, disembodied formulas. Similarly, quantum mechanics, like rela-
tivity theory, is said to introduce a system of purely mathematical
formulas, which cannot be interpreted either in terms of waves, parti-
cles, or any other visualizable things.

Nevertheless, it is easy to see that the difference between classical
mechanics and relativity mechanics has nothing to do with the sup-
posed difference between a “natural” and an “artificial” or “sophisti-
cated” theory. To characterize the difference between classical and
relativistic mechanics in this way is as incorrect as a similar judgment
on the difference between the geocentric and heliocentric theories in
astronomy.

Classical mechanics is very convenient for describing and pre-
dicting motions of bodies with velocities small in comparison with the
velocity of light. Such comparatively slow motions include the move-
ments of bodies we observe dmly, even the movements of the celestial
bodies such as the sun, moon, and stars. In order to describe these mo-
tions it is convenient to introduce the term “length of a body” without

153

modern science and its philosophy

specifying any frame of reference with respect to which this length
is to be measured. Similarly, we use tlie expression “two events occur
simultaneously” without requiring the specification of a frame of ref-
erence in order that the expression should have a definite meaning.

However, the situation becomes altered if we try to describe and
predict the motions of bodies having velocities comparable with the
velocity of light, for example, the fi-iays of radium, or cathode rays.
In order to formulate in the simplest way the laws governing such
rapid motions, it is found most convenient to drop the term “length of
a body” and introduce the new term “length of a body A with respect
to a body B“ where B has a determinate velocity with respect to A.
The definition of the “relative length of a body” will consist in the
description of the procedures of measurement involved, just as in the
case of the definition for the so-called “absolute length” of a body.
Since all these procedures of measurement are described in the thing-
language of daily life, there is no occasion to regard one of these defini-
tions as more abstract than the other. The definition of “relative
length” involves the use of observation terms just as does the definition
of “absolute length,” the sole difference being that the first definition
is slightly more complicated. The use of “relative length” in the de-
scription of the motions of bodies occurring in daily experience would
complicate those descriptions unnecessarily; but it would not make
them either too abstract or unintuitive. On the other hand, were we
to use the term “absolute length of a body” in describing the behavior
of bodies having velocities comparable with that of light, we would
also greatly complicate our descriptions; that is to say, our system
of physics dealing with such bodies would become very inconvenient if
we persisted in using the term ‘length of a body” according to the
formative rules by which the syntax of the language of classical physics
is determined. The most familiar and popular example of such a com-
plication is the necessity of introducing the terms “ether” and “ve-
locity with respect to the ether” into the system of physics. These terms,
however, remain in a sense isolated from most other terms of physics,
simply because no experiment can be set up by which we could deter-
mine the magnitude of this “velocity with respect to the ether.”

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modern physics and common sense

Einstein’s theory of relativity in effect introduces new formative
rules into the system of physics for the use of the term “length of a
body.” According to these rules the term “length of a body” can occur
in sentences only if the sentences also contain such qualifying expres-
sions as “with respect to a specified reference frame.” In this way super-
fluous terms like “velocity with respect to the ether” can be eliminated
from the language of physics, while at the same time the laws govern-
ing high velocities like those possessed by j8-rays can be formulated
in a very simple way.

S imilar considerations hold for the term “simultaneously.” In
classical mechanics it is used in accordance with a certain set of forma-
tive rules which do not require that sentences containing the term also
contain the qualifying phrase “with respect to a specified frame of
reference.” In relativistic mechanics we employ a different set of
formative rules; according to these rules the term “simultaneously”
may be employed only if the indicated qualifying phrase also
occurs.

These syntactical differences between classical and relativistic
mechanics are often expressed in ways tliat easily lead to misunder-
standings. Thus, it is sometimes said that classical mechanics con-
siders simultaneity in an “absolute sense” while relativistic mechanics
does so in a “relative” sense. It is advisable, however, to state the
matter intended by using the “formal idiom,” and to express the
difference in terms of the different formative rules according to which
the word “simultaneous” is used in classical and relativistic mechanics.
For if we talk of “simultaneity in an absolute and in a relative sense”
we are easily led to the meaningless question whether absolute simul-
taneity exists or not.

It is clear that there is no difference between these two sets of for-
mative rules in their being “abstract” or “intuitive” on the one hand,
or “natural” or “intuitive” on the other. The sole significant difference
between them is that the language of classical mechanics together
with its formative rules is more convenient for discussing motions of
bodies that occur in daily experience, while the language of relativistic
mechanics and its distinctive formative rules is more suitable for for-

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modern science and its philosophy

mulating the more inclusive field of phenomena which contains bodies
with high velocities.

Anyone who supposes that the formative rules of relativistic syntax
are artificial, nonintuitive, or abstract in comparison with the rules for
classical mechanics can readily convince himself of the contrary by
imagining himself in a world in which the phenomena of daily experi-
ence occur in a way somewhat different from the way they usually do.
It will then be evident that both in the case of quantum physics and
in the case of relativity theory, the laws alleged to be in accordance
with “common sense” will be of quite a different type from what is
usually maintained.

Let us, therefore, in the manner of H. G. Wells, imagine a world in
which the flight of a tennis ball ca nn ot be formulated and predicted in
terms of Newton’s laws. Thus we may suppose that the path taken
by a ball is not determined by the way in which it is struck with the
racket. We also suppose that the only law which can be established in
this world simply states with what percentage balls struck in a certain
way take a determined direction with a determinate velocity. Tennis
matches could be organized in this world just as well as in the ordinary
Newtonian world, and skilled players would return served balls more
often than those not skilled. Although the game would be played in
accordance with the ordinary rules of tennis, it would be evident to a
careful observer that even the most proficient players would often not
succeed in sending the ball in an intended direction even when the ball
is struck in the appropriate way.

In such a world neither the familiar man-in-the-street with his
well-known common sense, nor the laboratory physicists with a critical
attitude toward all “abstract” theories, would claim it to be a matter
of common sense that the laws governing the motions of tennis balls
should be formulated in terms of the expression “the position and
velocity of a tennis baU at the moment after it is struck.” For such an
expression would not occur in any of the laws with the help of which
the direction of flight of a struck ball could be predicted. Indeed, in this
imagined world the laws would require a specification of the way in

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modern physics and common sense

which a ball is struck, but would have no use for the specification of the
velocity a ball acquires on being hit. In brief, even everyday experi-
ence in this world would not be formulated in laws containing the
expression “ball with a determinate position and velocity.” The ex-
pression would not be employed in the language of daily affairs, and
would be taken to be as meaningless for everyday experiences as it in
fact is in the actual world of atomic physics. For in this imagined
world tennis balls behave in the fashion of the atoms and their nuclei
of our actual world.

The impression often current that the language of quantum physics
is artificial and contradictory to common sense arises from the fact
that this language is unnecessarily exact for use in the affairs of daily
experience. If, however, the things in daily experience behaved as ten-
nis balls would behave in our imagined world, this language would
be the one most suitable for discussing even the most familiar mat-
ters. In that case no one would dream of claiming that the language of
quantum physics is artificial or that it is incompatible with common
sense. It would be accepted as a very natural language indeed, and
would be judged to be as convenient and suitable for everyday mat-
ters as quantum mechanics is now taken to be for the phenomena of
atomic nuclei.

157

CHAPTER

philosophic misinterpretations of the quantum theory

1. The Origin of Philoiophie interpretations of Physicol Theories

AS soon as any new physical theory appears, it is used to con-
tribute something toward setting the controversial questions
of philosophy, the questions on which philosophers have
been working for centuries without coming a single step closer to
their solution. Numerous examples of such use suggest themselves.
When J. J. Thomson showed that every electrically charged particle
possesses inertia just as a mechanical mass does and gave a formula
for calculating the mechanical mass of a particle from its charge and
size, people deduced from this result arguments to prove that all
matter is only a phantom. They found in it an argument for the ideal-
istic world view and against materialism. Similar interpretations were
suggested when energetics arose and phenomena were represented as
energy transformations rather than as arising from collisions of masses.
The theory of relativity then introduced four-dimensional non-
Euclidean space instead of the three-dimensional Euclidean space in
which the directly observable processes of everyday life take place.
Later, wave mechanics described physical processes with the aid of
the probability concept, which has been often said to be a purely
spiritual factor, instead of with the aid of mass particles. Everywhere
it appears that the spiritual element is replacing the grossly material.

Such interpretations were attached with especial intensity to Niels

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ghilosophie misinterpretations of quantum theory

Bohr’s theory of the complementary nature of certain physical descrip-
tions, from which it was hoped that arguments for vitalistic biology
and for free will might be obtained.

If one scans all such interpretations, the empirically establishable
fact is found that they all further a movement toward a certain world
picture. It is not a case of different world pictures being involved; the
same one keeps coming up again and again.

Through the work of Galileo and Newton, anthropomorphic medi-
eval physics was expelled from conscious intellectual life. There re-
mained, however, an unfulfilled longing to bring about the unity of
animate and inanimate nature which had been present in medieval
physics but was missing in the newer physics. There was left only one
problem, for which no satisfactory solution could be envisaged: to
understand the processes of life in terms of physics. For that was the
necessary condition for a unified conception of nature after the dis-
appearance of the anthropomorphic conception of physics, which had
fitted in so well with the vitalistic conception of life.

Every crisis in the history of physical theories is associated with a
certain lack of clarity in their formulation, and this unfulfilled longing
bursts forth with great strength from the unconscious. Efforts were
made to complete the new physical theories by "philosophic interpreta-
tions’’ in order to proclaim the imminence of a return to the anthro-
pomorphic physics of the Middle Ages and a consequent reestablish-
ment of the lost unity of nature. Spiritualistic physics was to hold the
possibility of embracing the living processes also.

The assertion is often heard that there is also a philosophic interpre-
tation of physical theories in the service of a materialistic-metaphysical
picture of the world. However, this symmetrical conception of spiritual-
ism and materialism is a very superficial one. A “materialistic meta-
physics,’’ in general, does not exist today as a living intellectual current.
At most, it is represented for the domain of physics by those philoso-
phers or scientists who wish to make as wide a gulf as possible between
physics and biology, in order to obtain in the field of the living or the
social processes free play for a spiritualistic metaphysics.

If, on the other hand, one understands by materialism the belief

15?

modern science and its philosophy

that all processes of nature can be reduced to the laws of Newtonian
mechanics, then this is not a philosophic principle but a physical
hypothesis. True, it is a physical hypothesis that has been shown to be
wrong, but a physical statement it remains. This false hypothesis is not
accepted today by any of the philosophic schools that one is accus-
tomed to designate polemically as “materialistic"— neither by the
“dialectical materialism” of Soviet Russia, nor by the “physicalists”
that have come out of the Vienna Circle.

The process of the philosophic interpretation of physical theories in
the service of the spiritualistic conception of the universe can be an-
alyzed both psychologically and logically. From the psychologic stand-
point, the following, roughly, has been established: The physicist, like
every other educated person, acquires the remnants of prescientific
theories as a “philosophic” world picture, which in our cultural circles
consists mostly in a vague idealism or spiritualism as it is usually
learned from lectures on general philosophy. The principles of this
philosophy are unclear and difficult to understand. The physicist is
happy if he finds in his science any propositions that have in their
formulation some similarity to propositions of idealistic philosophy.
He is often very proud that his field of work helps him throw some
light on the general doctrines that are so important for this world
picture. Thus even the slightest similarity in the wording is enough
to induce the physicist to offer a proposition of his science as support
for the idealistic philosophy.

If J. J. Thomson speaks of “real” and “apparent” mass, the philo-
sophically educated physicist is eager to bring this mode of expression
into connection with the distinction between a “real” and an “apparent”
world. The statement that mechanical mass is only "apparent” mass is
then taken as confirmation of philosophic idealism, according to which
matter is only an illusion.

Of greater scientific interest is the logical structure of these philo-
sophic misinterpretations. The process of thought leading to them
consists of two steps. First, physical propositions that are really state-
ments about observable processes are regarded as statements about
a real, metaphysical world. Such statements are meaningless from the

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philosophic misinterpretations of quantum theory

standpoint of science, since they can be neither confirmed nor con-
tradicted by any observation. The first step is therefore the transition
to a meaningless metaphysical proposition. In the second step this
proposition, by means of a rather small change in wording, goes over
into a proposition which again has a meaning, but is no longer in the
realm of physics; it now expresses a wish that people should behave
in a certain way. This proposition is then no longer metaphysical, but
has become a principle of morality, of ethics, or of some other system
of conduct.

One can adduce numerous examples of such processes involving
two steps. As the simplest, we choose the well-known example of the
electromagnetic mass. J. J. Thomson formulated the purely physical
proposition that every electrically charged body possesses mechanical
inertia, which can be calculated from the charge. To this has been
added the hypothesis, likewise physical, that the entire mass of the
body can be calculated in this way. Philosophers then expressed this
as a metaphysical principle by saying: “In the real world there is no
mechanical mass at all.” This principle obviously has no scientific con-
tent. From it there follow no observable facts. As the second step, it
was asserted that the material world, as a mere illusion, is unimportant
in comparison to the world of the spirit, and that therefore man in his
actions can or should neglect any changes in the material world and
should devote himself to his spiritual perfection.

When influential groups express such wishes, the fact has a great
importance for human life, of course, and possesses a meaning, but
there evidently exists no logical connection with the electromagnetic
theory of matter, and the whole thing arises only through this mis-
interpretation with its two steps.

The essential part of the misinterpretation is the passage through
the “real” metaphysical world. The misinterpretation can therefore
be avoided only if one tries to set up a direct short circuit between
the physical principle and the moral principle. This can be done, for
example, through the consistent use of the “physicalistic language,”
which Neurath and Carnap have suggested as the universal language
of science.

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modern science and its philosophy

As understood in Carnap’s “logical syntax,” the source of these
misinterpretations is always the use of the “material mode of speech.”
The contrast between “apparent” and “real” mass is made to appear
as a statement about a fact of the observable world, whereas it is really
a syntactic rule about the use of the word “real.” Only the formula for
the connection between electric charge and inertia is a statement about
the observable world.

Quite the same logical structure is possessed by the misinterpreta-
tions of the relativity and quantum theories. The first has been em-
ployed to provide a basis for the belief in predestination, the second
to give scientific arguments for “spontaneity of action” and “freedom of
the will.”

2. The Complementary Conceptions of Quantum Mechanics and Their Interpretotions

The philosophic misinterpretations of quantum mechanics can be
best understood if we remember that the same tendencies are at work
here as in the interpretation of previous theories, and that the process
takes place along exactly the same lines, both psychologically and
logically.

First we must make clear the meaning of the complementarity
conception in physics.

One often reads the following formulation: “It is impossible to
measure the position and the velocity of a moving particle simul-
taneously.” The world, therefore, just as it is according to classical
mechanics, is filled with particles having definite positions and veloci-
ties; unfortunately, we can never attain a knowledge of them. This
presentation, in which the states of the particles play the role of the
“thing in itself” in idealistic philosophy, leads to innumerable pseudo
problems. It introduces physical objects, namely, particles with definite
positions and velocities, about which the physical laws of quantum
mechanics say nothing at all. These objects play a role similar to that
of the reference system that is absolutely at rest, which some wish to
add to the theory of relativity but which never occurs in any physical
proposition. In both cases the reason for this addition is that such
expressions were found useful in the earlier state of physics, and the

philosophic misinterpretations of quantum theory

school philosophy had made of them constituents of the “real world”;
therefore they must be kept forever.

Another way of representing the situation consists in saying that
particles “in general do not possess definite positions and velocities
simultaneously.” This mode of expression appears to me to have the
diflBculty that the combination of words “particle with an indefinite
position or velocity” transgresses the syntactic rules according to which
the words “particle,” “position,” and “indefinite” are ordinarily used
in physics and everyday life. Of course, there would be no objection
if a new syntax were introduced for these words for the purposes of
quantum mechanics. In that case, expressions like “particle with an
indefinite position” could be employed inside of physics without any
danger. And there exist many correct works on the quantum theory in
which this is the case. However, gross misunderstandings arise as soon
as this way of speaking is used in matters where it is no longer a ques-
tion of the quantum theory. We can bring about this transition to
other fields only by regarding the particle with an indefinite position
as a constituent of the “real world”— and then we are right in the
midst of the philosophic misinterpretations that were described in
Section I.

I believe that, as a starting point for a correct formulation of the
complementarity idea, one must retain as exactly as possible the
formulation set forth by Bohr in 1936.

Quantum mechanics speaks neither of particles the positions and
velocities of which exist but cannot be accurately observed, nor of
particles with indefinite positions and velocities. Rather, it speaks of
experimental arrangements in the description of which the expressions
“position of a particle” and “velocity of a particle” can never be em-
ployed simultaneously. If in the description of an experimental arrange-
ment the expression “position of a particle” can be used, then in the
description of the same arrangement the expression “velocity of a
particle” can not be used, and vice versa. Experimental arrangements,
one of which can be described with the help of the expression “position
of a particle” and the other with the help of the expression “velocity”
or, more exactly, “momentum,” are called complementary arrange-

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ments, and the descriptions are referred to as complementary descrip-
tions.

If one adheres strictly to this terminology one will never run the
risk of falling into a metaphysical conception of physical comple-
mentarity. For it is clear that nothing is said here about a “real world,”
nor about its constitution, nor about its cognizability, nor even about
its indefiniteness.

A great seduction to metaphysical interpretations lies in the fre-
quently occurring formulation of complementarity according to which
the “space-time” and the “causal” descriptions are said to be comple-
mentary. In this way the fact is often hidden that this again only means
the complementarity of position and momentum, or of time and energy.
By “causal description” we understand here only the description by
means of the principles of conservation of energy and of momentum,
which does not quite agree with what is usually understood by
causality. In popular presentations, among which are those of some
physicists, this is not always set forth clearly. This lack of clarity arises
from the use of the expressions “space,” “time,” and “causality,” which
as a kind of trinity play a somewhat mysterious role in idealistic phi-
losophy. If by “space-time description” is meant simply the assignment
of coordinates and time, by “causal description” the application of the
conservation principles, then this beloved terminology can be retained,
of course. But it then loses the charm of the mysterious and can no
longer be used to pave the way for a transition from physics to ideal-
istic philosophy, thereby favoring those misunderstandings described
in Section I.

If we are once in the midst of metaphysical formulations, we can
easily come to rather crass misinterpretations. As an example, I shall
give one by a very prominent physicist. A. Sommerfeld says ( Scientia,
1936 ):

If we treat the human body physiologically, we must speak of a corpus-
cular localized event. To the psychic principle we can assign no localization,
but must treat it— and this is also the opinion of psycho-physiologists— as if it
were present more or less throughout the body, just as the wave is connected
with the corpuscle in an unspecifiable way.

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philosophic misinterpretations of quantum theory

Here we may see with great clarity how every metaphysical formula-
tion of a statement of physics can be used with great ease to support
a statement of idealistic philosophy that only sounds somewhat similar.

To express the idea of complementarity for physics in closest as-
sociation to Bohr’s formulation, so that it will not lead to any meta-
physical misinterpretations but yet can be carried over to fields out-
side of physics, one will have to proceed somewhat as follows:

The language in which occur statements like “The particle is at this
place and has this velocity” is suited to experiences involving gross
mechanical processes and cannot be employed satisfactorily for the
description of atomic processes. However, one can give a group of
experimental arrangements for the atomic domain in the description
of which the expression “position of a particle” can be used. In the
description of these experiments— and in this consists the idea of Bohr
—the expression “velocity of a particle” can not be used. In the atomic
domain, therefore, certain parts of the language of gross mechanics
can be used. The experimental arrangements, however, in the descrip-
tion of which these parts can be used, exclude each other.

Meaningless metaphysical propositions immediately arise if one
says that "reality” itself is “dual” or displays “different aspects.”

3. Complementarity as an Argument for Vitalism and Free Will

Many physicists and philosophers have tried to make use of Bohr’s
doctrine of the complementarity of physical concepts in order to ob-
tain arguments for the impossibility of an understanding of biology and
psychology in terms of physics. Here we can distinguish something
like a psychologic and a biologic argument. The first runs approximately
as follows: If one seeks to describe a psychic state in terms of intro-
spective psychology, the state is so strongly altered by self-observation
that it is no longer the original state. It is not possible to be angry and
at the same time to observe and describe one’s anger. The existence of
a psychic state is incompatible with its observation.

The second runs something like this: If one wishes to describe the
state of a living organism by means of physical quantities, the measure-
ment of these quantities requires such a severe disturbance of the

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organism that it must be killed. The description of a living being
through physical variables is incompatible with its life.

The psychologic argument is basically a good one. It is a long-
recognized doctrine of every positivistic conception of science, in-
cluding that of A. Comte, that one cannot found any logically con-
nected psychology on principles obtained through self-observation.
One must go over to an objective observation of human actions and
movements of expression, as required by American behaviorism, and in
accordance with the logical analysis given by Camap and Neurath of
the statements concerning psychic processes.

If psychology is formulated in terms of behaviorism or physicalism,
the psychologic argument coincides with the biologic one.

If one applies the Bohr idea of complementarity, one can formulate
the role of self-observation in psychology somewhat as follows: There
are certain experimental arrangements in the field of psychology that
can be described with the aid of propositions and expressions obtained
from self-observation. There are other situations in our life that cannot
be described with these expressions. In this there is no contradiction.
As in physics, so in psychic life there are complementary situations, and
complementary languages for their description.

Taking this complementarity into consideration, one will easily see
what can be gained for the understanding of free will from the analogy
to the quantum theory. Even before Bohr’s discovery of complemen-
tarity, M. Planck had advanced the following argument for the com-
patibility of free will with physical causality: If a man could calculate
his future actions from the present pattern of the physical world, this
knowledge would react on his present state— for example, on the
molecules of his brain— and thus change his state. Hence there is no
predictability of the future. Hence free will cannot be in contradiction
to the physical causality of occurrences in the human body.

From this it only follows that a man cannot calculate his future
actions from the results of self-observation. It might still be possible,
however, for one to calculate beforehand the actions of other men, and
to do so even from purely physical observations.

If one applies here Bohr’s idea of complementarity, one can give

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^philosophic misinterpretations of quantum theory

to the whole matter a firmer logical structure. One can then say: Cer-
tain situations of human behavior are described with the help of the
expression “free will”; under other experimental conditions this ex-
pression cannot be used. We are, therefore, dealing here with comple-
mentary situations and with complementary descriptions, but not
with any contradictions. Bohr himself pointed out that his considerations
of complementarity cannot be used to provide an argument for “free
will”; they can only yield a useful representation of the epistemologic
status of the problem.

It seems to me, however, that there is also a certain objection to
the use of the words “free will” for the description of certain situations,
corresponding to the experimental arrangements in physics. Expressions
like “position of a particle” are expressions taken from the physics of
everyday life which, because of complementarity, remain suitable
for atomic physics only in certain special situations. Likewise, “free
will” would have to be an expression from the psychology of daily
life which in scientific psychology could be employed only under
certain experimental conditions. This, however, seems to me not to be
the case. “Free will” is not an expression from the psychology of daily
life; it is rather a metaphysical or theological expression. In everyday
life “freedom” is never anything other than “freedom from external
coercion,” or at most “freedom from intoxication and hypnosis.” This
has nothing to do with the philosophic conception of freedom of will.
If it is correct to say, following Bohr, that the expression “free will”
can be used advantageously for the description of certain situations,
this expression can refer only to the quite unphilosophic concept drawn
from the psychology of everyday life. Hence from this use no con-
clusions can be drawn about the philosophic freedom of will. It is only
necessary to put to oneself the question whether, for the general situa-
tion in which the concept of free will is used in practice, any change has
been created by quantum mechanics and the complementarity con-
cept. By this I mean, of course, the application of the freedom concept
to the question of the responsibility of a criminal, and to the related
question of the harshness or lightness of the punishment. One need only
formulate precisely die whole idea of complementarity and follow

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through carefully the whole chain of ideas up to the punishment of
the criminal to see at once that no consequences follow here for the
problem under consideration. It is therefore very questionable whether
it is appropriate to use the expression “free will” in the applications of
the complementarity idea to psychology.

If, however, in accordance with the new conceptions of behavior-
ism and physicalism, psychology is based on principles containing,
not statements about self-observation, but statements about the be-
havior of experimental subjects, then the complementarity considera-
tions in psychology as just described drop out, and psychology be-
comes a part of biology. In that case the psychologic argument of
Bohr reduces to the biologic one. It is, therefore, a question of whether
the behavior of living organisms can be represented by laws in which
only physical variables occur.

If one wishes to describe a living being physically, one must specify
the state of each of its atoms: this is Bohr’s starting point. The observa-
tions required for this description, however, involve physical disturb-
ances of the organism that are so great as to be fatal. The states of the
atoms of an inanimate body can be specified within the limits imposed
by the Heisenberg uncertainty relations, whereas the large protein
molecules with which life is associated are destroyed by disturbances
that would allow atoms to continue to exist.

Experiments by which the living organism may be described in
terms of the functions that characterize it as living are therefore carried
out under experimental conditions quite different from those of
experiments on the organism as a physical system. According to Bohr,
it is a question here of “complementary” e,\perimental arrangements,
which are described in “complementary languages.” Therefore, to
describe the phenomena of life in a language which is not that of
’ physics or chemistry is logically free from objections and does not
constitute a lapse into a spiritualistic vitalism.

This way of putting the matter, as given by Bohr, is very different
from that of most of his "philosophic interpreters,” and is certainly
tenable. In so far as its usefulness is concerned, some remarks can be
made. The whole argument derives its force from the fact that it is an

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philosophic misinterpretations of quantum theory

analogue of the argument that led from classical to quantum physics
and justified the statement that atomic processes cannot be described
in the language of classical physics. In order to establish limits for
the appropriateness of this analogy we shall therefore compare two
lines of thought.

First, in the transition to quantum physics one reasons as follows:
According to classical physics, one must be able, in principle, to devise
experiments permitting the measurement of the positions and the
velocities of individual particles veith arbitrary accuracy. But our
knowledge of atomic processes— for example, the Compton effect-
shows on closer analysis that the possibility of such measurements is
contradicted by experience. Hence atomic phenomena cannot be
described in the language of classical physics.

If we wish to extend this reasoning from the inanimate to the
animate, we must accept it as an experimental fact that an observation
by physical means, sufiSciently accurate to enable one to describe
exactly the physical state of the individual atoms of a living body,
represents so great a disturbance that it kills the organism. It follows
then that classical physics, aided by quantum physics (of inanimate
atoms), is inadequate for the description of the phenomena of life,
since it is incompatible with the application of physics to the living
organism that the latter should be killed by every act of exact
measurement.

The strength of the quantum theory lies in the fact that no hypoth-
esis about the atom based on classical physics could be found that
was in agreement with the experimentally testable behavior of observ-
able bodies. If the testing of a hypothesis about atoms through direct
measurements of their mechanical state (position and velocity) had
not been in contradiction with empirical facts, the hypothesis would
have remained within the framework of classical physics. Since, how-
ever, quantum mechanics does involve contradiction, it goes beyond
classical physics.

If we wish to retain the same chain of ideas for the transition from
inanimate to living bodies, then empirical evidence must be presented
to show that the exact physical observation of the atoms of a living

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^ body is incompatible with the known empirical laws for the behavior
of living bodies and with the physical hypothesis about tlieir atomistic
structure. As long as this evidence has not been submitted, it follows
only from Bohr’s train of thought that in biology, in the present state
of our knowledge, the complementarity mode of expression is possible
and perhaps even desirable. In contrast, for the transition from classi-
cal physics to quantum mechanics one can conclude that in atomic
physics the complementarity mode of expression is necessary.

4. Summorizing Remarks

From all that has been said, it is clear that Bohr’s complementarity
theory does not provide any argument for free will or vitalism. Like-
wise, one cannot derive from it any new conception about the relation
between the physical object and the observing subject, if we under-
stand the words “object” and “subject” in the sense in which they are
used in empirical psychology. In presentations of quantum mechanics
in which reference is made to this new role of the observing subject,
the word “subject” is understood in quite another sense. By “subject” is
always meant the measuring arrangement, which can be described in
terms of classical physics. What was shifted by the quantum theory
was the relation between the object of atomic theory— the atom or
electron— which cannot be described by means of classical physics, and
the measuring instrument, which can be described classically. The
observing subject, in the sense of empirical psychology, has no other
task than to read off the measuring instrument. 'The interaction be-
tween measuring instrument and observing subject can be described
classically, as far as we can say from the present state of physics.
The boundary line between the classical and the quantum-mechanical
descriptions lies between the electron and the measuring instrument.
Since within the region of classical description it can be displaced
arbitrarily, the boundary line can also be drawn between the measur-
ing instrument and the observer. But thereby nothing new is expressed,
since within the classical region the position of the section is arbitrary.

The great importance of Bohr’s complementarity theory for all
branches of science, especially for the logic of science, seems to me

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philosophic misinterpretations of quantum theory

that it starts out with a language that is generally understood and
accepted, the language used to describe the gross mechanical processes
of motion. Its significance lies in the fact that in its use all men are in
harmony. In physics this language is used in such expressions as “posi-
tion of a particle,” in the sense of gross mechanics. Atomic processes,
however, cannot be described in this language, as the new physics has
shown. Bohr has demonstrated in a careful analysis of modem physics
.that certain parts of the language of everyday life can nevertheless be
retained for certain experimental arrangements in the field of atomic
phenomena, although different parts are required for different experi-
mental arrangements. The language of daily life thus possesses comple-
mentary constituents which can be employed in the description of
complementary experimental arrangements.

There is no doubt that this idea is also a fruitful one for logical
syntax in general and deserves to be applied to other branches of
science. One would have to start out in psychology with the language
of everyday life and see whether, in the transition to more subtle prob-
lems, this language could be retained. One might perhaps start with
the “physicalistic” "protocol language” of Camap and Neurath and see
whether any parts of it are particularly suitable for describing certain
situations. Perhaps the symbol language of psychoanalysis is a sugges-
tion of such a partial language. The phenomenal language of which
Camap often spoke in his earlier works must be dropped as a general
language, but perhaps, as a constituent of a general language in the
sense of the Bohr conception, it can provide a satisfactory description
for certain experimental situations.

171

CHAPTER

determinism and indeterminism in modern physics

% A #HEN philosophers describe their standpoint with regard
\l\Mto a ne w physical the ory, their attitude is usually one of
Y f the following three; (1) the new theory contradicts the cor-
rect philosophic system and is therefore false; (2) the new theory
is a brilliant confirmation of the correct philosophic system and is there-
fore to be welcomed; (3) the new theory can be used for more or less
important improvements in the correct philosophic system and there-
fore possesses a certain value.

When the physicist attempts to continue outside of physics his
manner of forming principles and of verifying them through experi-
ments, he comes to the conception of science called l ogical empirici sm.
This conception has become fairly well known in recent years, es-
pecially through the work of the Vienna Circle. It is from this point of
view that I wish to examine a book ^ by Ernst Cassirer, since this is
the point of view most closely associated with the thinking of the
physicist.

No doubt many will demand a so-called “immanent criticism” of
a philosophic work. I believe, however, that such a demand usually
signifies only a plea of extenuating circumstances, and in the case of

^E. Cassirer, Determinismus und Indeterminismus in der modemen Phystk;
historische und systematische Studien zum Kausalproblem (Goteborg; Elanders
Bokhyckeri Aktiebolag, 1937).

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determinism and indeterminism in modern physics

a book as important as the present one this would be even derogatory.
For, at best, the result of immanent criticism of a book is the ac-
knowledgment that even if it is nonsense, it does have method.

Such rather scholastic criticism I will not attempt. Instead I want
to consider how one must judge Cassirer’s exposition from the stand-
point of logical empiricism, according to which only those statements
may occur in science that can be justified through logical derivation
or empirical tests.

According to this conception, philosophic principles, which are not
scientific in the above-mentioned sense, form a system of isolated
propositions from which there are no logical bridges to the system of
scientific propositions. Hence a system of philosophic principles can
never be either confirmed or refuted by new physical theories. Strictly
speaking, neither can it undergo any improvement. There is often
the appearance of improvement, but it can arise only from the fact
that an agreement in emotional coloring is taken for a lo^cal agree-
ment. 'This is frequently made possible because the physical principles
are formulated in a metaphysical, rather than a purely physical, lan-
guage. In such a case, however, one should not say, for example, that a
physical theory is in contradiction to a philosophic system, but rather
that the metaphysical formulation of the theory appears to be irrecon-
cilable with the philosophic principles under discussion.

When one reads this book by Cassirer one gets at once the impres-
sion that the foregoing considerations about the relation between sci-
entific and philosophic principles do not apply to it. Most of Cassirer s
assertions about the new physical theories are acceptable throughout
from the standpoint of the physicist and its extension into logical em-
piricism. I might say even more. Cassirer’s statements about the new
quantum mechanics are less full of metaphysical prejudices and con-
tain fewer transitions from physical to metaphysical language than
some statements made by physicists in their professional writings or
in speeches on festive occasions. Cassirer’s statements are almost all
scientific statements, as understood by logical empiricism. Isolated
systems of propositions, such as those that play the chief role in the
school philosophy, hardly occur. Hence there cannot arise any appar-

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modern science and its phiiosophy

ent contradiction between physical and philosophic principles. What
does induce in me a critical state of mind is a certain background
against which the presentation is brought into relief, a background
which is distinctly separated from the basic assertions, but which
through its terminology, foreign to science, makes me feel again and
again that the author regards all that he says as only rather superficial
utterance, the deeper meaning of which he intimates but does not
wish to discuss.

For this reason I have designated Cassirer’s mode of thinking,
which is to be seen not only in his present writing but also in his earlier
works, a "disintegration process within the school philosophy.”

This remark in my book “The Law of Causality and its Limits” “
has often been looked upon as an unfavorable criticism of Cassirer’s
point of view. Quite the opposite is the case. In the book mentioned I
wanted to show that the “disintegration” of the school philosophy
forms a necessary preliminary condition for the progress of science
from the individual sciences to a unified science. Precisely in the case
of the present book it can be made clear what the disintegration process
that Cassirer carries out consists in, and, furthermore, we can also see
how this process remains within the school philosophy, at least in its
emotional background. Practically considered, Cassirer’s conception
of the principles of physics is almost exactly that of logical empiricism.
However, at the end the sharply drawn contours are a little blurred in
the direction of transcendental idealism— which is perhaps only a
question of style. It seems to me that this shading of the outlines is a
little dangerous, since we know that the reader is often influenced more
by the emotional undertone of an exposition than by its logical and
empirical content.

Some of the basic conceptions of Cassirer are in a remarkable
manner related to, or almost coincident with, the conceptions formed
by the logical empiricism of science. Cassirer repeatedly points out
that science creates auxiliary concepts, such as force or atom, in order
to be able to formulate conveniently the theories it has set up at a

*P. Frank, Das Kausalgesetz und seine Grenzen (Vienna: J. Springer, 1932);
La Loi de causalitS et ses Unites (Paris: Flanunarion, 1936).

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d[,eterininism and indeterminism in modern physics

certain time, but that at later times these auxiliary concepts freeze into
essences, “ontological concepts,” which are retained even if they are
no longer very convenient in the state of science at that time. This,
however, is precisely the criticism leveled at the existence concepts of
the philosophers by the Vienna Circle, so often attacked as “anti-
philosophic.”

In my essay on the death of Ernst Mach,* I characterized as the
enduring nucleus of Mach’s teachings his struggle against the “idoliza-
tion of auxiliary concepts.” The French Catholic philosopher J. Mari-
tain, at the Thomistic Congress in Rome in the summer of 1936,
characterized as a great service that was essential also for Catholic
philosophy the fact that the aim of the Vienna Circle and of the whole
movement of logical empiricism was "to disontologize scienc e."

The disintegration of the school philosophy in Cassirer’s work is
revealed very clearly in his general conception of the law of causality.
He believes that there is no such law that can be formulated like a
definite law of nature. In his opinion the law of causality asserts only
that there exist, in general, laws of some sort in nature. Kant tried to
formulate causality also with respect to its content, by asserting, for
instance, that for every process there exists another “which it follows
according to a rule.” Cassirer rejects not only the very special world
formula of Laplace, but also the far more general formulation of Kant;
there remains only the formal requirement, also attributable to Kant,
that nature be describable with the help of simple rules. Here, how-
ever, there is left hardly any contradiction to Ernst Mach’s purely
positivistic conception of science.

Another fundamental feature of Cassirer’s conception is that the
form of the law of causality and the concepts of what one calls an
“object” mutually condition each other. This also is a basic thesis of
logical empiricism, and one that has been taken over from positivism.
It is only that logical empiricism gives to this thesis a more formal
turn: Ae form of every physical law depends on what variables are

*P. Frank, "Die Bedeutung der physikalischen Erkenntnistheoiie Machs fur
das Geistesleben der Gegenwart,” Natutwisseruchaften 5, 65 (1917). This essay
is Ghapter 2 of the present hook.

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modern science ond its philosophy

introduced to describe the state of a system. It may happen that with
respect to some variables for a certain domain of phenomena there
exist deterministic laws, but not for other variables. This consideration
leads, in the extreme case, to the conventionalistic assertion that
through the introduction of certain variables, the law of causality can
be made valid; this assertion, however, states nothing at all about
nature but is merely a "de fi nition of the state of aflairs.” That is to say,
in the language of Cassirer, that through the introduction of an ap-
propriate concept of the "object” one can always bring about the
validity of a law of causality. Like the positivists, Cassirer escapes this
conventionalism only by requiring that the causal laws be “simple.”
The concept of simplicity remains exactly as vague in his case as in the
case of the positivists. And the requirement of the "existence of natural
laws,” which, according to Cassirer, constitutes the real content of the
general law of causality, involves that indefinite concept of “simplicity”
in a very fundamental way. The assertion that the general law of
causality can be expressed only vaguely was one of the essential theses
of my book “The Law of Causality and its Limits,” which was there-
fore termed “hyperskeptical” and “antiphilosophic” by many. Exactly
this character, however, is possessed by Cassirer’s conception of
causality, which I have therefore designated approvingly as “dis-
integrating.” Since Cassirer understands by determinism only the re-
quirement that simple laws exist in nature, he cannot find any con-
tradiction, of course, between this requirement and modern quantum
mechanics. In place of the laws of classical physics we have there other
equally exact laws. Cassirer’s presentation is therefore not a criticism
of modem physics from the standpoint of “philosophic determinism,”
but neither is it an attempt to improve "philosophic determinism” with
the help of modern physics. What Cassirer does is to conduct an in-
vestigation on the question of how the mles and laws of physics have
changed their form in recent years because of quantum mechanics.
This investigation is carried out with a thorough knowledge of the
subject. Except for a few obscure points, it is in agreement with mod-
em physics and, naturally, can never come into contradiction with its
principles. For Cassirer does not set up any philosophic deterministic

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do^erminism and indeterminism in modern physics

laws as judges over the principles of physics; rather, he is prepared to
consider every exact law as fulfilling the deterministic postulate.

Surely this conception is completely tenable, and surely it is more
useful for understanding modem physics than are the attempts of many
philosophers to formulate the law of causality more precisely and then
to interpret physical theories so that they fit into this scheme. An ex-
ample of such a method is the well-known, in many respects sagacious,
book by the physicist and philosopher Crete Hermann, “The Philo-
sophic Basis of Quantum Mechanics.”* She starts out with Kant’s
special formulation of the law of causality and tries to formulate the
principles of quantum physics in accordance with it, in such a way that
for every process there exists another one which the first follows ac-
cording to some mle. She is then forced, however, to introduce as
“cause” a process which, aside from the effect for the sake of which it
was introduced, cannot be observed, so that the law of causality be-
comes a mere tautology. Such a fraitless procedure is avoided by
Cassirer through his very general comprehension of determinism.
Nevertheless, many distinctions between classical and modem physics
are perhaps lost by it. To express the law of causality, following
Laplace, as the possibility of predicting future processes is also fmitless
unless one says how the states of a physical system are to be described.
One can try, however, to formulate the possibility of prediction in ac-
cordance with experimental possibilities, on the understanding that
one describes only such processes as can be actually carried through.
For example, one can say that, according to classical physics, by a suf-
ficient refinement of the aiming mechanism one can strike the center of
a target to within any desired degree of approximation; whereas, ac-
cording to the quantum theory, if one bombards the target with elec-
trons it wall never be possible to suppress their scattering below a cer-
tain degree. We can therefore say in a certain sense that in the field of
observable processes the new atomic physics is no longer deterministic
in the same way as classical mechanics.

In its general features, Cassirer characterizes quite appropriately

*G. Hermann, Die naturphttosophUchen Crundlagen der Quantenmechanik
(Berlin, 1935).

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modern science and its philosophy

the change in physical laws due to modem physics by saying that now
it is not die concept of “thing” but the concept of “law” that stands in
the foreground, and that the so-called physical reality, the physical
object, is only created by the law which we obtain from observation.
He says:

We no longer deal with a being, self-contained and absolutely de-
termined, from which we directly read ofiE the laws, and to which we can
attach them as its attributes. What really forms the content of our empirical
knowledge is rather the aggregate of observations which we group together
in a certain order, and which we can represent through theoretical concepts
of laws according to this order.

As far as the dominion of these concepts extends, so far extends our
objective knowledge. There is “objectivity” or “objective reality” because,
and in so far as, there are laws— not conversely. From that it follows that we
cannot speak of a physical "being” otherwise than subject to the conditions
of physical cognition, including its general conditions as well as those special
conditions that are valid for its observations and measurements.*

Reading such deliberations, one comes to think that Cassirer ac-
cepts completely the positivistic conception of the quantum theory, ac-
cording to which concepts like “position” or “velocity” of a particle can
be used only under certain experimental conditions, while the formulas
of physics only give directions for bringing such observations into
relation with one another.

The reader of Cassirer’s book is further strengthened in this opinion
when he comes to the statement;

If it turns out that certain concepts, like those of position, velocity, the
mass of a single electron, can no longer be filled for us with a definite
empirical content, they must be eliminated from the theoretical system of
physics, no matter how important and fmitful their contributions may have
been.

Often Cassirer even employs a terminology that is linked with the
nineteenth-century positivism of Kerre Duhem:

We choose the concepts in such a way that through them the phenomena
will be described as completely and unequivocally as possible, that through

* E. Cassirer, op. cU., p. 164.

178

determinism and indeterminism in modern physics

them the phenomena will be preserved. This requirement of ri

tt>aiv6na>a goes back to the dawn of scientific physics.

However, when Cassirer tries to describe the real role of such
concepts as particle, position, and velocity in quantum physics, he
expresses himself rather vaguely. He presents the more or less provisory
formulations of various physicists— Schrodinger, Heisenberg, Dirac—
but does not decide in favor of any one of them as logically the most
satisfactory. It seems to me that it is best to adopt the latest formula-
tions of Niels Bohr, which he gave at the second Congress for the
Unity of Science, held in Copenhagen in 1936, and which are fully
compatible with the formulations of logical empiricism. Bohr said there
quite clearly that concepts like “position of a particle” and “velocity of
a particle” are expressions of everyday language which can be used in
atomic physics only under special experimental conditions; moreover,
"position” and “velocity” can be used only under conditions which are
mutually exclusive. The term “particle” never occurs in atomic physics
equipped with all the properties that it has in everyday language and
in the physics of macroscopic mechanical processes. In the descrip-
tion of many experiments there does occur a particle which sometimes
has a definite position, sometimes again a definite velocity. The fact
that in such cases the term “particle” is used at all is due to the con-
nection with the motion of large bodies. Actually, however, this term
is used in a somewhat different sense, or, more exactly, according to
different syntactic rules.

From the lectures that were held at the aforementioned Congress,
it is clear that in the complementarity conception of atomic physics
it is only a question of introducing a new syntax for the words “posi-
tion” and “velocity of a particle” which is different from that of every-
day language.' In this connection Strauss pointed out that it is not at
all a question of introducing mysterious new objects like “particles
without a definite position.”' All these lectures made it plain that,
although there may exist a difference between the view of Bohr and

’ See the lecture of M. Strauss.

'See, besides the lecture of N. Bohr, those of M. Schlick, V, Lenzen, and
myself.

179

modern science and its philosophy

that of the adherents of logical empiricism with regard to the applica-
tion of the complementarity principle to biology and psychology, there
is certainly no difference in their ideas on the meaning of comple-
mentarity in physics.

It seems to me that Cassirer started out with a formulation of the
complementarity conception in atomic mechanics that was somewhat
vague, both from a physical and from a logical standpoint. This defect
crops up now and then also in bis general discussion. It can easily be
shown that there are many places in Cassirer’s book that cannot be
understood from the standpoint of logical empiricism, a fact which is
connected, in my opinion, with his leaving the scientific analysis pre-
maturely and going over to metaphysics. One gets an inkling of this
transition in statements such as:

But a concept like that of material point, from the very nature of the
matter, can never be understood as the copy of a physical object; it is a
"form” the meaning and content of which consist in their usefulness for
the theory, in their ability to lead to simple and rigorous laws for phe-
nomena.

What does it really mean to call the material point a “form”? Evi-
dently it means in the language of physics that the statements in which
the term “material point” occurs must have a definite syntactic form in
order to be suitable for the representation of observations, and that
this syntactic form in quantum mechanics is no longer the same as in
classical mechanics and in everyday language. Cassirer, however, does
not use the word “form” expressly in the sense of “syntactic form.” As
he uses it, it is a reminiscence of the Kantian terminology, in which
space and time are “forms of experience.” Here the word “form” is
taken neither in the sense of “spatial form” as in everyday language,
nor in the abstract sense in which, say, one speaks of the “form of a
mathematical equation,” but in a quite specific sense which really
occurs only in Kantian philosophy and may lead to serious misunder-
standings. If one calls the material point a “form,” one is making use
of a language that does not fit well into the scheme of physical proposi-
tions. To be correct, one ought to say: “ ‘Material point’ is an expression

180

d^erminism and indeterminism in modern physics

which, combined with other words according to definite syntactic
rules, is appropriate for the representation of observations.”

It is easy to see that Cassirer, in other places, really expresses him-
self as if, behind the world of relations which the theory sets up among
observations by the help of its symbols, there existed another “real”
world which we can approximate only imperfectly.

Immediately after the statement quoted above, that outside of the ^
connections among observations one cannot speak of a “physical
being,” Cassirer says:

This “being” has thus lost its ultimate permanence. It is to some extent
included in the process of physical cognition and is to be considered only
as a limit to which this process tends, but which is never quite reached.

The “real world,” that characteristic fiction of every school philos-
ophy, remains in Cassirer’s conception as a “limit.” It would be con-
sistent, however, to take this role from it also, for even in this respect
one cannot speak of it in a scientific way.

No sooner has Cassirer spoken of this “limit” than he again makes
statements in a quite positivistic sense. One sees here very clearly the
disintegration of the school philosophy, which, however, has still left
untouched a certain dark background, namely that "limit” and those
“forms.”

That tliis (in my opinion not entirely consistent) critical attitude
toward metaphysics prevents him from representing the scientific
sense of quantum physics with complete clarity is to be seen in several
places in Cassirer’s book.

Cassirer represents the facts stated by the Heisenberg uncertainty
principle in the following way:

According to the conditions under which the observation is made, the
object shows us to some extent a difierent aspect. We obtain, according to
the choice of the measuring instrument and the use we make of it, various
pictures of the event. No single observation can open up and hold out to us
at one time the totality of possible aspects. Through every particular measur-
ing arrangement certain features of the event are, so to speak, screened from
us, as for example the wave nature or the particle nature of light, whereas
others are brought out in their place. What the thing is in an absolute sense,

181

modern science and its philosophy

outside of the circumstances of observation as realized in the various experi-
ments, is something about which we no longer obtain an answer.

Through this mode of expression Cassirer depicts the situation in
quantum mechanics as though it were a question of things that are
absolute, but that cannot be comprehended in all their aspects with one
measuring arrangement. In this way he brings into physics terminology
from the philosophy of transcendental idealism, which is entirely for-
eign to Bohr’s complementarity doctrine in its physical form. Quan-
tum physics says only that with certain experimental arrangements
concepts like “particle with a definite position” or “particle with a
definite velocity” can be defined. In other words, the physical processes
that occur with these experimental arrangements can be predicted
through statements in which one refers to “a particle with a definite
position” or “a particle with a definite velocity,” but there is no ar-
rangement for which one can predict processes through statements
involving “a particle with a definite position and velocity.” This, how-
ever, does not mean that there are particles of which, because of the
defectiveness of our apparatus or because of malicious natural laws, we
cannot measure all the characteristics (position and velocity); it means
rather that such combinations of words as “a particle with coordinates
X, y, z, and velocity components v^, v” must not be introduced into
the language of physics. If we were to say that the things correspond-
ing to such combinations of words nevertheless exist as absolute, but
unknowable, things, we should be going over into pure metaphysics
and destroying every bond with experience, which is surely not Cas-
sirer’s purpose.

Cassirer thus characterizes often very pertinently the scientific-
logical structure of the laws of quantum mechanics, but then he al-
ways formulates them again in the language of idealist philosophy,
thus robbing them of their clearly delineated scientific meaning and
opening the door to misinterpretations in the direction of an abso-
lutistic metaphysics.

That Cassirer basically does not accept this metaphysical interpreta-
tion of the quantum theory is to be seen from the determination with
which he rejects the opinion that from this theory any conclusions can

182

fl^terminism and indeterminism in modern physics

be drawn in favor of free will or even of moral responsibility. Much
more clearly than many physicists have done, Cassirer sees through
the deceptiveness of all such arguments and characterizes them very
appropriately. He says, for example:

In itself it would be very bad for ethics and its dignity if it could not
maintain authority except by watching for gaps in the scientific elucidation
of nature and, so to speak, creeping into these gaps.

In these words Cassirer ably characterizes the repeated attempts of
philosophers and many physicists to use the lacunae in science for the
introduction of supernatural factors.

At another point he says:

If the idea of ethical freedom were threatened by these ideas [of
rigorous natural laws], it could get no help from quantum mechanics. As far
as this problem is concerned it is immaterial whether we think that a natural
phenomenon is governed by rigorous dynamical laws or whether we assiune
merely a statistical regularity. For even from the latter standpoint it would
be determined to such an extent that the ostensible freedom, the free will,
could find no refuge in it. An act which, from the physical standpoint, is
to be regarded as not completely impossible, to be sure, but as improbable
in the highest degree, is one that need not be taken into consideration in
the domain of our will.

And quite tersely and precisely:

The problem of nature and freedom remains the same whether we take
the general laws forming the concept of nature as dynamic or as statistical
laws.

This separation of the question of natural laws from the question of
ethical freedom is treated by Cassirer in a way that is very similar to
that of Schlick in his Froblems of Ethics* which was attacked as being
extremely positivistic. Also the rejection of the use of gaps in the laws
of physics for introducing spiritual factors arises from positivistic lines
of thought and is to be found in a quite similar form in my book “The
Law of Causality and its Limitations.’'

^M. Schlick, Fragen der Ethik (Vienna; Springer, 1930); tr. by David R 3 nain
as Problems of Ethics (New York: ]^ntice-Hall, 1939).

183

modern science and its philosophy

This attitude of Cassirer toward the question of the relations be-
tween quantum mechanics and ethics must be valued all the more
highly in view of the fact that there have been many physicists who
supported enthusiastically this misuse of the quantum theory, and
sometimes even initiated it. As a contrast to Cassirer’s rigorously sci-
entific argument on this question I should like to bring up a few
sentences from a lecture by the famous English physicist J. H. Jeans.
He says: ,

The plain average man . . . believed, among other things, that he was
free to choose between the higher and the lower, between good and evil,
between progress and decadence. To many, Victorian science seemed to
challenge all such beliefs. It knew nothing of higher nor lower, progress nor
decadence; it knew only of a vast machine, which ran on automatically and
of its own inertia, as it had been set to run on the first morning of the crea-
tion . . . VVe now begin to think that this challenge was a mistaken one,
that the universe may be more like the untutored man’s common-sense con-
ception of it than had seemed possible a generation ago, and that hu-
manity may not have been mistaken in thinking itself free to choose between
good and evil, to decide its direction of development, and within limits to
carve out its own future.®

At the end of his book Cassirer indicates of what use his philos-
ophy of quantum mechanics may be. He believes that the change of
viewpoint between wave theory and particle theory which the quan-
tum theory brings about within physics is analogous to the change
of viewpoint that takes place when one goes over from scientific con-
siderations to ethical or esthetic ones. This analogy has been suggested
also by many physicists, such as P. Jordan and Crete Hermann, and
even by Bohr, although very cautiously and with many restrictions.
Whether one looks upon it as deep and fruitful or as merely super-
ficial is more a question of guessing future developments than of sci-
entific argument.

To summarize: Cassirer’s book is to be welcomed from the stand-
point of logical empiricism as a highly successful attempt to continue
the adjustment of the traditional idealist philosophy to the progress of

® J. H. Jeans, “Man and the Universe,” in Scientific Progress (London; G. Allen
and Unwin, 1036), pp, 37 ff.

184

^terminism and indeterminism in modern physics

science, which in my opinion can end only with the complete disinte-
gration of the tradiHongl philosop hy. The ingenious arguments of Cas-
sirer, presented in clear, understandable language, will be read with
great benefit by every physicist and will be useful in correcting many
misinterpretations of modem physics. For the adherent of the school
philosophy the book signifies, h'ke many previous writings of Cassirer,
a way out of an impasse.

185

CHAPTER

how idealists and materialists view modern physics

% k ME know today that nature can be described and understood
\i\MQOt “mechanistically” but only through abstract mathemati -
f Y oaI foTinuI as. Great significance has been attached to this
revolution for the philosophic world view. The argument is that since
a mathematical formula is something purely mental, the world can no
longer be understood in a materialistic sense. Materialism must be
superseded by idealism. The phvsi c^ of the twentieth cent ury is a vic-
tory for the “spiritualistic” or, as it is sometimes less clearly expressed,
i dealistic wor ld view.

This viewpoint has its representatives among both the id ealists and
th ^ material ists. The former rejoice at the unexpected aid they have
received for their world view from the progress of science itself. The
latter blame modem physics for abandoning the paths of progress
marked out by G alileo and N ewt on and promoting the return to the
dark views of the Middle Ages.

We will cite from the writings of a few English and German authors
to illustrate the point of view of the idealists, and from the works of
Soviet authors, the apprehensions of the materialists.

In his well-known book The Mysterious Universe, the famous Brit-
ish physicist. S ir James Jeans say s, for example:

The signal for the revolution was a short paper which Einstein published
in June 1905. And with its publication, the study of the inner working of

186 ^

4)ow ideolists and materialists view modern physics

nature passed from the engineer-scientist to the mathematic ian . . . The
essential fact is simply that all the pictures which science now draws of
nature, and which alone seem capable of according with observational fact,
are mathematical pictures . . . Nature seems very conversant with the
rules of pure mathematics, as our mathematicians have formulated them in
their studies, out of their own inner consciousness and without drawing to
any appreciable extent on their experience of the outer world . . . Our
remote ancestors tried to interpret nature in terms of anthropomorphic con-
cepts of their own creation and failed. The efforts of our nearer ancestors to
interpret natme on engineering lines proved equally inadequate ... It
would now seem to be beyond dispute that in some way nature is more
closely allied to the concepts of pure mathematics than to those of biology or
of engineering ... In any event, it can hardly be disputed that nature and
our conscious mathematical minds work according to the same laws. She
does not model her behavior, so to speak, on that forced on us by our whims
and passions, or on that of our muscles and joints, hut on that of our thinking
minds , . , The concepts which now prove to be fundamental to our
understanding of nature . . . seem to my mind to be structures of pure
thought, incapable of realization in any sense which would properly be called
material . . . To my mind, the laws which nature obeys are less suggestive
of those which a machine obeys in its motion than of those which a musician
obeys in writing a fugue, or a poet in composing a sonnet . . . The universe
can be best pictured ... as consisting of pure thought, the thought of
what, for want of a wider word, we must describe as a mathematical
thinker.^

The physicist and astronomer Jeans has here made use of this turn
from a “mechanistic” to a " mathemati cal" understanding of physics to
favor a religiously tinted metaphysics. When the professional German
philosophers, on the other hand, deal with this revolution in science,
we find them erecting a “scientific” metaphy sics on this foundation.

To illustrate this tendency we will quote a few passages from
B. Bavink’s Science and God. The author stresses that the fundamental
laws of physics are t oday statements about probab ility.

But a TTiathfliq^ tical probabil ity is not a physical reality like a tempera-
ture or field strength or what not. With this new interpretation, the whole
material .notion nf suhstanca disa ppears in our h ands. What remains then of

^ J. H. Jeans, The Mysterious Universe (New York: Macmillan, 1930), pp. 106,
135, 138, 143, 145 ff.

187

modern science and its philosophy

the plain, real, hard, sharp, heavy, etc. matter? A certain probability depend-
ing on formal mathematical laws, that energy or impulse are observable at
a certain world-point.

The physicist of today has learned— an enormous advance from the point
of view of his world-view— that his atoms or electrons or what not, are no
longer to be regarded as rigid lumps of reality, from which no path can be
found into the mental and spiritual sphere; he sees, on the contrary, that
all these structures are forms in perpetual flux, which are only of interest even
to him as regards their form. With this view, every variety of materialism is
superseded.®

In this mathematical conception of nature, Bavink, like Jeans, sees
the foundations of a n idealistic philosoph y of physics and hence of
science as a whole. The only difference is that Bavink uses somewhat
more technical philosophic terms.

One task Bavink proposes for an idealistic philosophy of nature is
the following:

It still remains to be shown how the material world is to be deduced
from the purely psychical data. It is obvious that spiritualism has hitherto
always faffed in this respect. It has never succeeded in deducing even the
properties of a hydrogen atom from data of this kind. What is new in the
present situation is the fact that such a proposal no longer appears so
completely absurd as it did even twenty years ago. For that which hitherto
presented an insuperable obstacle, namely the “rigid lumps of reality” of
ordinary atomic theory, has been resolved into pure form, and a mathematical
form is in itself something psychical, it belongs, as Plato already saw, directly
in the realm of the Logos, which is behind all things . . .

There it stands; the hard, cold sober world of matter with its atoms, the
existence of which is today proven beyond a doubt. It is impossible to pass
it by, and it is time for all idealists Anally to accept this fact and give up their
fruitless attempts to avoid it. Matter will only be finally subjugated by mind
when we are really able to understand it as the product of psychical powers.
Merely to postulate this as a fact, which is all Aat spiritualism has hitherto
done, is not of the slightest use; matter and its worshipers, the materialists,
simply laugh us out of court saying: here is a single atom, the simplest of
all, the hydrogen atom. Show us what you can do! Show us how we are to
imderstand it as the product of purely psychical potencies— then we will
believe you. Now it appears as if spiritualism today can actually pass this

‘ B. Bavink, Science and God, English translation by H. S. Hatfield (London:
BeU, 1933), pp. 68, 71.

188

how idealists and materialists view modern physics
*

test. I will not maintain that it has already passed it, but I believe it to be
undeniable that it is very close to doing so, and has every prospect of
success.®

Some professional philosophers look upon modem physics as a
direct return to the anthropomorphi c, animistic physics of the Mid-
dle Ages, as it was practiced by Aristotelian scholasticism. Thus Aloys
Wenzl, Professor at the University of Munich, says in his essay,
“Metaphysics of Modem Physics”:

And in this manner the human struggle for insight in the world wiU
have described a circle, or more correctly a spiral. The examination of nature
began with an anthropomorphic representation of the material world, in that
souls were ascribed to material things, and the relations between them were
viewed as expressions of psychic relationships of love and hate. The tendency
to reification led farther and farther away from such early representations,
freed physics more and more from such images and of necessity led ever
closer to a mathematical examination of nature. For there are only two
possible ways of making the facts and the laws of experience meaningful.
They must either be treated according to psychologic laws or associated
with the ideal forms of mathematics. Modem physics has followed the
second method to the very limit. But if more is desired, if assertions about
their meaning are to be made, the mathematically expressed relationships
must be explained, which would be a return, on a much higher plane, to he
sure, to the original method, if not in physics, then in metaphysics.*

When we notice how a philosopher of the twentieth century “ex-
plains” the physics of his day, we will see that the “idealisti c” explana-
tion is not so far removed from the “spiritualistic” or mystical. In the
same essay, Wenzl says:

It is clear that the concept of matter has changed completely . . . Only
the m athematical me thod itself actually defines the sphere of the materfal
world . . . But we can no longer associate an idea of something dead, with
this material world. If we do wish to make an assertion about its essence, it is
much sooner a world of elemental spirits which are bound in their relation-
ships and their formation of wholes to certain rules of the spiritual realm
which are mathematically comprehensible; or to put it in other words, it is

’‘Ibid., pp. 93, 95.

*A. Wenzl, “Metaphysik der Physik von heute,” Wissenschaft und Zeitgeist
(Leipzig; Meiner, 1935), No. 2, p. 30.

189

modern science and Hs philosophy

a world of lower spirits whose reciprocal relationships can be expressed in
mathematical form. We do not know what kind of relationship this mathe-
matical form signifies, but we do know the form. Only the mathematical
forms themselves or God could know their inner significance. A very alert
metaphysician might explain them at best by analogy to known psychic
relationships.’

All these utterances show what great hopes the supporter s of ideal -
ism have had in the crisis in physics of the twentieth century. But just
as some political systems adopt idealism as the foundation for their
philosophy, so the supporters of Marxism acknowledge materialism
as a foundation for their world view. When we read the writings of
the spiritual leaders of Russian Marxism, we see that the crisis in
physics and its utilization as propaganda for idealism are viewed with
concern and alarm.

Lenin published in 1908 a book under the title “Materialism and
Empiriocriticism: Notes on a Reactionary Philosophy.”® In the fifth
chapter, entitled “The Latest Revolution in Science and in Philosophi-
cal Idealism,” Lenin speaks of the changes brought about in the con-
ception of matte r bv the ene r getic and electromagnetic theories. The
physicists inclined toward idealism often formulate the results of these
new conceptions as follows:

The atom is demateiialized. Matter disappears.

And the Russian philosopher N. Valentinov in his book “Ernst Mach
and Marxism” (1907) draws the following inference with reference to
a world view:

The assertion that a scientific explanation of the world is found in straight
^latglialism, is now no more than a myth, and a foolish one at that.

Says Lenin:

There is not the slightest doubt about the association of the new physics,
or rather a certain school of the new physics, with the school of Mach and
other types of a modem idealistic philosophy.

The nature of the crisis in modem physics consists in the overthrow of

® Ibid., pp. 28, 29.

® English translation (New York: International Publishers, 1927).

190

%how idealists and materialists view modern physics

old laws and fundamental principles. Objective reality outside of conscious-
ness is rejected and materiali.sm is replaced by ideaUsm and agnostici sm. Mat-
ter has disappeared. This is the way the basic and typical difBculty created by
the crisis is expressed.

Even in the year 1922 when Lenin was already at the head of the
Soviet Government of Russia, he was much concerned about the dan-
gers for materialism that might and did arise out of the crisis, thereby
imperiling the foundations of Communism. At that time it was the
relativity theory that played the most important part in the crisis in
physics.

On December 3, 1922 Lenin wrote in the journal Under the Ban-
ner of Marxism:

We must keep in mind that as a result of the revolution taking place in
science today, reactionary philosophic schools and tendencies are likely to
arise. Therefore, the journal Under the Banner of Marxism must be con-
cerned about this revolution in modem science; otherwise, fighting material-
ism would be neither fighting nor materialism.

If the great majority of middle-class intelligentsia stand behind Einstein,
who is not taking an active part in the fight against materialism, then this
holds not only for Einstein, but for most of the great scientists since the
end of the nineteenth century.

We find the same apprehensions and the same fight if we examine
textbooks that have been introduced in Soviet colleges for teaching
materialism. Thus we find in the textbook Dialectical Materialism : '

The attempts made to think of .motio n without matter and of force
without underlying substance are laying the foundation for idealis m and
p]firipa|j<Tn At the present time we see the furthering of these same idealistic
tendencies. As a result of their association with Einstein’s theory of relativity
many are inclined to imagine motion without matter.

And again:

In place of the old unchangeable atoms there has appeared a system of
movin g electron s. Therefore, say the "Machians,” matter has disappeared.
But actually, more exact principles are replacing primitive physical laws.

^ M. Mitin, ed., DUdekticheskU Materializm ( Moscow Philosophical Institute
of the Communist Academy, 1934), vol. 1, pp. Ill, 55.

" 191

modern science ond its philosophy

Yet the followers of Mach say: There is no objective knowledge . . . The
latest quantum mechanics strengthens the concept of causali tv. and makes
corrections in the old concept. The Machians, however, declare that causality
has disappeared.

In the Russian materialistic literature there is a great deal of criti-
cism of the new physical theories, particularly quantum mechanics, on
account of their mathematical and formalistic n ature. In effect, the line
of approach is much like that of the German and English idealists—
such as Bavink and Jeans— except that the materialists are naturally
critical about the replacement of mechanics by mathema tics as an
“idealistic” trend. I will cite as evidence an article entitled “Chemistry
and the Structure of Matter” which appeared in a Russian literary
journal, Krasnaya Nov. The author, Orlov, says:

Quantum mechanics is today still tmder the spell of the fetish , mathe-
matics. This means that the method of quantum mechanics is of a formal
T nathp.matical nat ure. The mathematical pattern permits the building of a
bridge that unites empirical facts furnished by spectroscopy with the be-
havior of electrons, atoms, and molecules. But up to now we have no physical
explanation for the formulas of quantum mechanics. Instead of that, it is
often proposed to abandon the search for an interpretation of physical laws
and to replace physical representations with abstract mathematical symbols.
It is in this that the fetish, mathematics, consists.

It is remarkable how often scientists with sympathies for idealism,
philosophers with scientific inclinations but of a spiritualistic back-
ground, and advocates of materialism as a tool for achieving poUtical
goals agree with one another in so many essential points.

We have seen in Chapters 5 and 6 that the transition from mecha -
nistic to mathem atical physics was the result of the positivistic co n-
ception of science and that it had nothing to do with the twentieth-
century tende ncy toward idealism and metaphysic s.

But it may well be, and is often maintained, that positivistic physics
•Contains an element of spiritualis m nr idealisTn Positivistic physics
consists in the last analysis o f propositions about observations o r per-
ceptions. But then, so it is often said, it asserts something about the
psychic. It has completely abandoned materialism and has become a

192

\how idealists and materiolists view modern physics

science of the mind, exactly like psychology. In fact, Ernst Mach built
up all the sciences out of relationships among sensation s.

Many, therefore, look upon positivistic physics as a varie ty of sub-
iective ideali.s m. which declares that science can never assert anything
about the actual world, but only about subjective sense impressions.

In the above-mentioned book. Materialism and EmpiriocrUidsm, Lenin
represented Mach’s doctrine as a direct continuation of Bisho p Berke -
ley’s philoso phy. He also blamed this doctrine for depreciating the
actual world and for promoting the view that behind the world of
sense impressions, about which alone science can assert something,
lies the real world, which, however, is inaccessible even to science.
According to this view, Mach seeks to strengthen the belief that the
real world can only be explored through extrascientific or superscien-*^
tific sources of knowledge such as metaphysics and religion.

This view of Mach’s doctrine, however, is completely contradicted
by Mach’s actual intentions. To be sure, it must be admitted that his
terminology may sometimes be the cause of such confusion. Also many
of his disciples were in effect inclined toward idealism, perhaps because
of pressure to conform to the prevailing ofiBcial philosophy, according
to which everything smacking of materialism was strictly taboo.

For Mach himself, however, the sensations with which he built
up the entire science were in no contradiction to the actual world that
seemed inaccessible to reason. For him these sensations, which to avoid
confusion he very often termed "elements,” were the building material
he wished to use to create a unified system of science; this could be
accomplished if one crossed from one field of science to another, say
from physics to physiology.

For Mach, there was no way in which the difference between the ^
apparent world and the real world could be scientifically formulated.

Yet the gross mechanistic philos ophy stood in no logical contradiction
to Mach’s conception. The bodies of daily experience with which
mechanism constructed its world were also nothing else than a complex
of sensations like sight and taste. The question whether there really
is a matter (a thing-in-itself) that is different from the sensation has
no meaning for science, since no experiment can be performed that

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modern science and its philosophy

might possibly settle the question. Every proposition about a gross
material thing can also be expressed about sensations. Thus the whole
of mechanistic physics can be translated into the language of Mach.
A logical contradiction exists only between a metaphysically conceived
Machism, which is then subjective idealism, and a metaphysically con-
ceived materialism, which accepts only matter as having existence. But
this doctrine was invented by idealists to refute materialism, and was,
in any case, hardly representative of the thought of scientificaUy
minded materialists.

The school philosophers (see Chapter 4) did not have to wait for
the relativity and quantum theories of the twentieth century to mis-
construe the transition from me chanistic to mathematical the ory. They
succeeded in doing this with the physics of the nineteenth and earlier
centuries. On more than one occasion diey made use of the explanation
of M ach’s doct rine as subjective idealism. It was even simpler than
that. Wherever they saw something mathematical they tried to ex-
plain it as an idg ^istic f.le.m p.nt inside materialistic physics.

Hermann Cohen, for example, the leader of the neo-Kantian school
of Marburg, says that mjchanics has acquired a more spiri tual char-
acter when such subtle mathematical concepts as the differential cal-
culus had to be used to formulate its laws.

In the critical supplement to the seventh edition of F. A. Lange’s
“History of Materialism” (voL 1, pp. 504 ff.) Cohen says:

The road of research leads straightway to idealism. Materialism is being
destroyed at the roots of physical concepts, and it is mathematics that is
leading in the emancipation, which promises to be a lasting one . . . Reality
is the Real in mass, force and energy— the reality of infinitesimally small
quantities. There are no other means by which we could even denote the
real of mass and force for Newtonians, or the real of electric charge for
dynamicists; much less can we explain these realities in another way. There
is no other means than the differentials. The infinitesimal is not only the
origin of every quantity but also the origin of being itself, of the real . . .
At the roots of physical concepts materialism was destroyed and the libera-
tion was achieved by mathematics. The old Platonic union of physics and
mathematics has proved its eternal strength. The mathematical ideas . . .
offer the solution of the fundamental question of philosophy— the question.
What is science?

194

^ how idealists and materialists view modern physics

But we have seen in Chapter 5 that the i dealistic int erpretation of
science, when taken seriously, is the first step in the return to the
animistic anthropomorphic science of the medieval scholastics.

Positivism, on the other hand, particul arly logical positiv ism, pre-
vents the crisis in the mechanistic philosophy from spreading to the
scientific world view as a whole. It shows that the abandonment of
mechanistic physics does not imply the need for a return to the anthro-
pomorphic physics of the Middle Ages. And right here something has
happened that seems rather paradoxical. All those that advocate a re-
turn to pre-Galilean science, whether it be under the name of “ideal-
ism,” “holism,” or “organicism,” or even under the name of “race”
or “nation,” fight with great ardor for the r etention of the mechanist ic
philosophy in the field of physics, and condemn the positivistic physics
as an aberration.

Evidence for this can be found by merely turning the pages of the
“Journal for the Whole of the Natural Sciences,” which was published
in Germany under the Nazi government from 1935 on. Its purpose was
to fight agains t positiv i sm in s cience. Its main line of attack was to en-
courage the struggle of “German” science against “French rationalism”
and “English empiricism.” Organismic philosophy is generally regarded
as specifically “German.”

A few passages from K. Hillebrand’s programmatic article, "Posi-
tivism and Nature," may be cited here. They will make clear how an
overestimation of mechanistic physics served in the fight against posi-
tivism and in behalf of organismic science.

Mechanism was a planned world picture constructed upon a principle;
positivism accepts without choice every experience into the sum of its ex-
periences. It accepts to be sure mechanistic explanations, as the equivalent
of sense perceptions, but it denies as a matter of course the significance of
every explanation, and gladly disavows them, for its aim is only description
... I therefore ask, is not the principle advantage of positivism over
mechanism tied up with as great a disadvantage? Is it really necessary or
even pleasing to exchange a pictural concept of a mechanistic explanation
for a pure mathematical formula, which transcends all perception? The
breakdown of mechanism into positivism— very interesting as intellectual
history— is an event, it seems to me, that is at present almost everywhere en-

195

modern science and its philosophy /

tirely misunderstood. And yet the principles of scientific method will never
be determined without its clarification.

And now the author embarks upon an inspired glorification of
mechanistic physics. He says:

He who understands the running of a machine, say a clock, based on the
complete dependence of rigid bodies on spatial conceptions, has genuinely
satisfying knowledge. It is the mistake of pnsiHvi.sm that it is .iblp.J-n take this
intention of Democritus as just one among other arbitrary hypotheses. It is
also unfortunate for the development of positivism that it retains the ob-
jectivistic bias of mechanism and has surrendered its only virtue, its pure,
clear picturization.

As is almost always the case with those favoring an idealistic-
organismic science, the enthusiasm for the mechanistic physics in its
most obsolete form is coupled with a strong aversion for the applica-
tion of non-Euclidean and multidimensional spaces. Hillebrand
continues:

Mechanis m is Euclidea n science. Relativism of non-Euclidean spaces, on
the contrary, is the favorite child o f positivi sm. A four-dimensional space or
a space with curved radii is just as logical for pure abstract thought as the
Euclidean; indeed the dissolution of space and time into mere abstract mathe-
matical formulas seems to be a distinct gain to this other type of human
being. The overwhelming eternal advantages of Euclidean space as against
these abstract arts ought not to be forgotten.

The reason for the glorification of “mechanistic” physics by the ad-
vocates of organicism is that for their argument they need the applica-
tion of a kind of physics that is as narrow as possible and therefore
most unsuited for the more involved events. Says Hillebrand:

It is evident from what has been said above that according to our way
of thinking mechanism is far superior to positivistic empiricism— so long as
it does not attempt to explain living matter. Besides, since Science has
abdicated in this respect, there is nothing lost; . . . the value therefore of
exact scientific research is not attacked, in so far as it is restricted to “dead”
matter nature. The human mind possesses two sufiicient types of knowledge:
the explanatory and the understanding. "Anschauun^ in the explanatory
sense is the mechanistic explanation of nature, the representation of bodily
form in a EucUdean space-time relation going far beyond positivistic sense

196

^how idealists and materialists view modern physics

perception and yet conceivable or pictorial in a narrower sense of sight and
taste sensation. The understanding type of knowledge is “Anschauun^ in
a wider sense, perception not as sensation, but rather as a palpable human
event that need not be "sensible.”

The German word Anschauung has two meanings, both of which
are used in this quotation. It means, first, “optical perception” or “pic-
tural representation”; second, however, it means “mental intuition” or
“empathic understanding.” This ambiguity makes the word Anschauung
a favorite term in idealistic metaphysics. It provides a philosophic
basis for the “intuition” of the totalitarian leader.

The tendency is very clearly seen to allow mechanistic science to
pass as the only "explanatory” type of knowledge that is useful for exact
science, so that it might be easier if necessary to introduce the so-called
“understanding” type of knowledge (intuition) in the sciences of
human conduct.

Logical empiricism, as opposed to this, stresses the unitary nharnrtpr
of science. It is not interested in splitting human knowledge into
“mechanistic-explanatoiy” and “imderstanding-intuitive” types. Our
modem logic of science depicts the factual process of successful knowl-
edge and scientific rep resentati on. Mechanistic explanation and intui-
tive understanding both are popular and rather superficial types of
scientific representation, but by no means particularly profound types
of knowledge.

197

CHAPTER

logical empiricism and the philosophy of the Soviet Union

% A #HEN 1 speak of philosophy in the Soviet Union, I mean
\ /%^only the system that is officially taught in all schools as
y Y pliilnsophy— ‘‘ Hialpirtical materia lism.” abbreviated to diamat.
Of course, in the writings of physicists, mathematicians, and biologists
one can find many remarks associated with the logic of science. These
are mostly only echoes of the views predominant in European and
American science. Besides the official diamat, no other consistent con-
ception of science has developed in the U.S.S.R. If one wishes to dis-
cuss the features that are characteristic of the intellectual life of Soviet
Russia, one must speak only about diamat, concerning which there are
prevalent in European science very unclear and often greatly dis-
torted views.

At first sight, it appears that diamat is extremely hostile to the vari-
ous forms of logical empiricism. This attitude is shown especially by
the following examples:

Empiricism is styled in a stereotyped way “crawling Ai^ricism,”
because it can never rise to the formation of a scientific system. The
various forms of neopositivism and logical empiricism are all branded
with the label “ Machis m." and, as such, are sharply condemned. It was
perhaps an ominous event for the history of philosophy in the U.S.S.R.
that Lenin set forth his philosophic views in a book directed against
the Russian followers of Mach and Avenarius— the book Materialism

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logical empiricism and Soviet philosophy

and Empiriocriticism.^ In 1935 the twenty-fifth anniversary of the ap-
pearance of this book was celebrated by all philosophical societies and
journals of the U.S.S.R. Because in it the doctrines of diamat were
elucidated by being contrasted with the conceptions of Mach, the
opinion was established in the official philosophy of the U.S.S.R. that
Machism-was a movement especially hostile to diamat, and hence to
be attacked vigorously. In reality, Lenin took issue with Machism be-
cause it is in many respects related to diamat, and he considered it
especially suitable for him to bring out his own teachings very sharply
by means of a polemic against it.

Because in the teachings of Mach everything is built on the per-
ceptions as elements, Lenin saw in them a degenerate form o f the sub -
T^^alism nf RfrkHfyi who had denied the re ality of the world
of experiences and thu s hsd-made room for the acceptance of a super-
natural world. On the other hand, because of the connection of
Machism with the enlightenment philosophy of the eighteenth century,
its predilection for contact with the physical sciences and its aversion
to the introduction of any anthropomorphic factors or “psychic” tend-
encies into science, Machism was reproached with having a “mecha-
nistic narrowne ss” which rendered it particularly incapable of encom-
passing social and historical events.

If we ask what is the attitude of diamat toward the movements
which have arisen from the synthesis of Mach’s positivism and Rus-
sell’s logic, we need only open the latest textbook of diamat in the
U.S.S.R. for information.' There we find it asserted, in effect, that the
newest Machists want to deepen Machism by the use of symbolistic
methods. They regard science as a game with empty symbols and thus
make it incapable of embracing the colorful fullness of the real multi-
form world. Idealism, mechanism , an d logic ism are only three ways of ■, /
leading people to a fictitious supersensual world and of. r estraining
them from occupation with the practical questions of the real world.
These three doctrines therefore, like religion, ar e npinm for the people,
putting them into a narcotic sleep which shows them a faded picture

^English translation by David Kvitko (London, 1927).

^M. Mitin, DUdektlcheskS MaterUdizm (Moscow, 1934).

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modern science and its philosophy

of tie real world. Philosophers who teach idealism, mechanism, and
logicism are in the service of th e bourgeoisie, just li ke the clergy, and
make their disciples unfit to work for the social reorganization of the
world.

While one gets from these statements the impression of a funda-
mental antipathy, yet scientific and sociologic considerations indicate
that this attitude of diamat is rather of a polemical and tactical nature,
and that it must also contain many elements which are closely related
to the ideas that we represent.

L ogical empi ricism developed primarily in the struggle against the
idealistic metaphysics of thf* .-rhonl philos ophy, which with its odd
mixture of faded theology and ob solete science has fulfilled a very
definite social function. The main struggle of diam at is also against this
metaphysics and this function. In a German textbook of diamat we
find “metaphysics” described as “an examination of the psendn-renl
surface , without penetrating into the essential.” Since this description is
in fair agreement with logical empiricism, we must expect to encounter
still other similarities.

The main points of a scientific doctrine related to logical empiri-
cism which we find in diamat are perhaps the following: ( 1 ) Science
should be “ materialisti c.” but not “mechanistic”; (2) the criterion for
the truth of a proposition should be only its confirmation in actual life,
the doctrine of “ concrete tr uth”; (3) the propositions of science are
to be understood not only from their logical connection with the prop-
ositions of the previous stages of science, but also from the causal con-
nection of scientific pursuits with other social processes. The investiga-
tion of this causal connection is carried on by a special factual science,
the sociology of science.

Here we wish to consider only the first two of these points.

( 1 ) First of all, we must be quite clear as to what diamat means by
the word “materialism.” What we generally understand by this word
as used in popular and even in scientific writings is t he conception of
all natural phenomena, including human evolution. . a.s analogous to a
machin e. This view would be called by diamat “mechanistic mate-

200

' • IkrUtHtomniricism and Soviet philosophy

rialism” or “mechanism," and is very strongly opposed. If we look up
the definition of the word “materialism” in the official textbooks of
diamat, we find, roughly, the following: “By materialism’ is meant the
conception that science speaks of a world that is completely indepen d-
<»n t nf any grTiitrarinps c, a world that is neither the creation of a world
spirit, as the obje ctive idealism of Hegel h olds, nor the creation of the
individual consciousness, as the subjective idealis m of Berke ley as-
sumes.”

From this form of the definition of materialism, which simply es-
tablishes the objective character of scientific principles, we shall not be
able to draw any very specific conclusions of the materialistic concep-
tion. If, however, we observe how this definition is applied in practice,
we find that all scientific propositions are to contain only terms that
occur in statements about observable facts. The description of a
process is of use to science only if all of the observable aspects of the
process are embraced. In particular, the part played by the so-called
psychic processes is not to be emphasized one-sidedly; that would lead
to “idealism.” If, to take an example given by a textbook on diamat, it
is asserted that the great power station on the Dnieper, the Dniepro-
stroy, is the product of the engineering plans, the matter is being de-
scribed idealistically and one-sidedly. The materialist will say: “Besides
the plans of the engineers, a decisive part is also played by the new
social organization introduced by the communist revolution, the new
conditions of the workers, etc.” Everything in the world that is de-
scribable through intersubjective expressions is called “matter” by
diamat.

This is not to say that matter actually has the properties which
Newtonian mechanics or even the newer physics attributes to mat-
ter. Such an opinion would be “mechanical materiali sm.” According
to diamat, every investigation of the world that makes use of inter-
subjective expressions is an investigation of matter. The properties of
matter reveal themselves to us only in the course of the development of
science. They will never be completely known to us as long as there
are new laws to be discovered.

This conception comes very close to the viewpoint that science is

201

modern science and Its philosophy

based on an intersubjective language, which Neurath and Camap have
designated more precisely as the physicalistic language. Just as, for
physicalism, the biologic or psychologic propositions are “physical in
the broadest sense," so for diamat the propositions about the develop-
ment of life and even about human history are propositions about
matter. However, just as physicalism does not claim that psychology
can be reduced to actual physics, so diamat does not say that the social
development of mankind can be reduced to those laws of matter that
have been discovered by physics. According to diamat, sociology itself
discloses new laws of matter.

Diamat seeks, however, to set up quite general laws for matter,
laws which are to hold for physics as well as for biology and sociology. ^
For this purpose it takes the three laws which Hegel formulated for
the processes of thought, and from which he also made laws for living
and inanimate nature because he believed that the whole world is the
product of thought. Marx and Engels turned Hegel’s teachings upside
down and began by setting up his three dialectical laws of thought
as the laws for matter. In this way they founded diamat, “dialectical
materialism.” The three laws are “the unity of opposites, the transi-
tion from quantity to quality, and the negation of the 'negation.” We
see that they still wear their idealistic eggshells. Their application to
reality is often very much forced, and from their consequences there
results what L. Rougier^ once called “Soviet my sticism." With these
three laws of dialectics, originating in idealism, diamat often strays
from the path of establishing the properties of matter through the
methods of exact research. Today a determined struggle is being
carried on within diamat against the “trivializat ion" of dialectics.

Such rather indefinite principles can often serve to order to some
extent the empirical material in fields that are still only slightly de-
veloped, like sociology. If, however, they are applied to sciences where
we possess better ordering principles, they at once reveal their im-
perfections.

Because of these dialectical laws, diamat bears within itself the
germ of jdealis m. Even in the U.S.S.R. it must perpetually struggle

'L. Rougier, Les Mystiques politiques contempor^es (Paris, 1935).

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logical empiricism and Soviet philosophy

against "idealistic deviations,” which in recent years have received the
name "menshevizing idealism” after the political party of the Men-
sheviks. Diamat wages continually a “war of two fronts” against ideal-
ism and mechanism without being able to mark out unequivocally the
boundaries separating it from these two deviations.

If it carried on this war of two fronts consistently, it would have
to discard the idealistic eggshell of Hegelianism, the exaggerated opin-
ion of the significance of the three dialectical laws. On the other hand
it would have to avoid the desc ription of matter as something exis ting
objectively— which is also, in the last analysis, an idealistic concep tion
—and instead would speak of in tersubjective p ropositions. Then it
would approach more and more closely the concept ion represented by
lo gical em piricism, especially by the Vienna Circle. For these groups
carry on the same two-front war, against the i dealistic school phil os-
ophy and against the belief tha t Newtonian mechanics in its orig inal*^
form is a basis of all science.

Though, therefore, in our opinion, the dialectical laws do not have
the importance for a modem conception of science ascribed to them by
diamat, we must nevertheless admit that something in what it calls
“dialectical thinking” is quite in line with our ideas.

This “dialectical thinking” is characterized by Lenin in his re-
marks on Hegel’s works simply as thinking which has the necessary
elasticity not to stick to a definite scheme, but which builds itself a new
scheme corresponding to the given stage of development of science.
This kind of dialectical thinking is demanded also by logical
empiricism.

(2) The second point essential for the understanding of diamat is
the “doctrine of concret e truth." According to this doctrine, the trath
of a proposition can never be judged by its abstract formulation, but
only by examining the practical conclusions that can be drawn from
it. Whether the idealists or the materialists are right can be judged only
by seeing what consequences the two doctrines have for practical life.
This conception is related to American pragmatism. 'The textbooks of
diamat try to distinguish it from pragmatism by saying that pragmatism

modern science and its philosophy

always means a “bourgeois,” that is, an individualistic practice, a test in
the life of the individual— in “business life,” as they often add derisively.
Diamat understands by test, above all, the test of a principle in social
life— in revolutionary practice, as they put it.

From this doctrine of “concrete truth” one can understand the much-
discussed attitude of diamat toward religion. By religion is never to be
understood an abstract system of principles of faith. A thing of that
sort cannot be tested for truth. By “religion” is always meant a con-
crete institution, as, for instance, the institution of the church. This
can be investigated to determine whether it has socially desirable in-
fluences or the opposite. Definitions of religion like “a feeling of one-
ness with the universe,” “devotion to a higher duty towards humanity,”
are rejected by diamat. One textbook remarks scornfully that European
philosophers, on the basis of such definitions, call even communism
itself a religion. By religion should be understood a concrete organiza-
tion which seeks to propagate the belief in a supernatural being among
men and thus to deter them from the struggle against their oppressors.
From this point of view one must judge the struggle against idealistic
philosophy an d against Machism and log icism. To this “doctrine of
concrete truth” Lenin attributed a great importance for the practical
political struggle. One must never hold fast to abstract formulas such
as: for the defense of the fatherland or against the defense of the
fatherland, for parliamentaiianism or against it. One must rather ex-
amine in every individual case the practical consequences arising from
such a demand and see whether they are favorable to the goal pur-
sued— hence, for Lenin, to the rise of the working class to power.

Lenin, however, applied this doctrine not only to political but also
to scientific principles. He insisted that propositions such as “Matter
is infinitely divisible,” or “ Matter is composed of indivisi ble atoms,”
are never to be labeled as true or false; they are to be judged by their
practical consequences, which can also change in the course of the
development of science.

The doctrine of concrete truth, if it is formulated conceptually,
and wherever it is applied exactly, is nothing else than the view that
the truth of a proposition can only be judged if the methods of testing

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logical empiricism and Soviet philosophy

it are given. If somebody states a proposition and fails to state the con-
ditions, observable in practice, under which he would be ready to ac-
cept it as true, then it is a proposition that is not scientifically applicable
—it is meaningless for science. With the doctrine of concrete trut h,
diamat is therefore defending a standpoint which is very closely related
to that of positivism and p ragmatism.

The conception held by many representatives of diamat, that
logistics is only a formalistic game which avoids having to do with
reality, is perhaps correct in the case of many metaphysically inclined
logicians. It is certainly not correct for the Vienna Circle, which uses
logistics only as an ai d to a r a dical empiricism and p ositivism.

In any case, the doctrine of concrete truth will some day be ap-
plied in the U.S.S.R. also to tlie teachings of science. Then it will be
said: In our time it is no longer appropriate to embrace the new empiri-
cal and positivistic groups with the idealistic school philosoph y in one
concept, “the bourgeois conception of science.” The patterns that
Lenin set up for a concrete situation of struggle should not be regarded
as general patterns, suitable for the representation of scientific develop-
ment. It will then turn out that there are very fundamental ties between
diamat and logical empiricism.

An analysis of the present situation leads to the conclusion that
to designate the lo gical empiricis m of today, or logistic neopositivism,
as “idealistic” or “mechanistic” Machism would be the same sort of ab-
stractly schematic conception as if one were to label diamat “Hegelian
idealism” because of the historical connection with Hegel, and for that
reason to reject it.

The creative scientific work, particularly in chemistry, physics,
and biology, that enjoys favorable conditions for development in the
U.S.S.R. and is in a state of rapid growth, still has very little practical
effect on diamat. In this situation lies the danger for diamat, which
may develop in isolation from science like the European school philos-
ophy, which also claims to give direction to science but succeeds only
in becoming more and more estranged from science, and consequently
languishes.

If, in the U.S.S.R., diamat will strive to cooperate with concrete

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modem science and its philosophy

science, those tendencies in it that point toward logical empiricism will
be strengthened. It will be obvious that the two-front war against ideal-
ism and mechanism can really be carried on consistently only from
the standpoint of critical positivism; otherwise one will surely slide
again into metaphysics to the left or to the right.

206

CHAPTER

why do scientists and philosophers so often disagree
about the merits of a new theory?

I F, in seeking an answer to the question that heads this chapter, we
put the preliminary question, “Do they really disagree?” my answer
is: At the beginning they do, mostly, but by and by the disagree-
ment weakens and finally the philosophers come to agree too com-
pletely. Frequently just at this moment the physical theory in ques-
tion turns out to be doubtful to the physicist. He advances a new the-
ory and the whole cycle of disagreement and agreement begins again.
If we succeed in understanding this periodically recurrent cycle we
have performed a great step toward the understanding of the interac-
tion between science and philosophy.

The divergenc es between physicists and philosophers have become
very clear recently. We have only to glance at the discussions about
space, time, and causality connected with relativity a nd the quantum
theory to see this. There are a great many people who believe that
these divergencies are characteristics of our twentieth-century physics.
In order to counteract this erroneous impression I shall start by dis-
cussing the attitude of scientists and philosophers toward the CopCT-
nican world system at a time when it was news. My point is that the
dispute of that time was of the same character as the dispute of toda y.

Copernicus published his system in the middle of the .sixteeiilh
QgQtuiy. A century afterwards this system was condenmed by the

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modern science and its philosophy

Ro man Inquisition as “pTiiio snphinally faisfi .” During this century the
Copemican system was taught in the universities and presented in
the oflBcial textbooks as a remarkable achievement in science which was
—unfortunately— “philosophically false.” This attitude is illustrated by
some sentences from a textbook of astronomy of 1581 written by the
Jesuit C. Clavius:

One may doubt whether it would be preferable to follow Ptolemy or
Copernicus. For both are in agreement with the observed phenomena. But
Copernicus’ principles contain a great many assertions that are absurd. He
assumes, for instance, that the earth is moving with a triple motion which
I cannot understand. For according to the philosophers a simple body like
the earth can have only a simple motion.

After setting forth a number of arguments of the same type the author
concludes:

Therefore it seems to me that Pto lemy’s geocentric doctr ine must be pre-
ferred to Copernicus’ doctrine.

In spite of the agreement with the observed facts the Copemican
system had to be rejected because it was in contradiction with certain
principles which were regarded as firmly established. For instance, a
simple body like the earth can have only a simple motion, such as a
rectilinear or circular one. Or, to quote a second principle of the same
type: We see that every piece of earth falls downwards along a straight
line; therefore the earth as a whole cannot possess a circular motion.
For it was an established principle that to every particular kind of
matter there corresponded a particular type of motion.

All these principles were parts of Aristotelian physics. 'They orig-
inated from generalizations of observation, just like any physical
theorems. 'They belonged, however, to an earlier state of physical sci-
ence. At the time of Copernicus they were already in a state of “fossili-
zation”; they were believed to be eternal tmths which could be derived
from pure reason. Every statement of science that was in disagreement
with these principles of Aristotelian physics was called “philosophically
false.” In this sense the Copemican system could be declared “mathe-
matically true” but “philosophically false.” This meant only that it was

'disagreement between scientists and philosophers

in agreement with the observed facts but in disagreement with the
principles of Aristotelian philosophy or physics— physics being a part
of philosophy.

It may be objected that this was the opinion of a Jesuit and ortho-
dox believer in scholastic philosophy. I shall quote, therefore, the state-
ment of a very progressive man of that time. Fr ancis Bac on has been
called in the textbooks of philosophy the very father of empirical
science. He says, in 1622:

In the system of Copernicus there are found many and great incon-
veniences; for both the loading of the earth with a triple motion is very
incommodious and the separation of the sun from the company of the
planets with which it has so many passions in common is likewise a diffi culty
and the introduction of so much immobility into nature by representing the
sun and the stars as immovable ... all these arc the speculations of one,
who cares not what fictions he introduces into nature, provided his calcula-
tions answer.

If we compare this judgment of an empirical philosopher with that
of the follower of Aristotle we perceive this difference: the self-
confident statements of Aristotelian physics now have faded into rather
vague statements of so-called common sense. We no longer derive from
profound metaphysical principles the conclusion that the sun must
possess the same type of motion as the planets, since it is of the same
nature. It is just a “difficulty” to separate the sun from the company
of the stars, since they look so similar.

The philosopher’s attitude toward physical science had, however,
remained essentially unchanged: physical theorems that are in con-
tradiction with certain established general principles have to be re-
jected, even if these physical theorems are in agreement with all ob-
served facts. The scholastic philosopher just as well as the advocate
of empiricism upheld the distinction between “ scientific truth ” and
“philosophic truth ." The truth of a physical theorem in the first sense
has to be checked by experiments. The truth in the second (the philo-
sophic) sense depends upon whether the theorem is compatible with
certain established principles.

In this sense the Copemican system was declared to be “mathe-

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modern science and its philosophy

matically true” but “philosophically false,” And this severe judgment
has been passed again and again by philosophers upon new physical
theories. Let us direct our attention to Bacon ’s characterization of
Copernicus’ personality:

Copernicus was a man who did not care what fictions he introduced into
nature provided liis calculations answer.

We cannot help remembering how many philosophic reviewers have
charged the authors of rec ent physical theo ries (particularly relativity
and quantum theory), with the same thing. We can perhaps under-
stand this divergence in the attitude of philosophers and physicists
most clearly if we examine the example of Newton’s phy sics. For in
this case we are able to pursue the fate of a great theory from its birth
to its death.

As a starting point I quote a judgment on Newton by a great
philosopher who was Newton’s contemporary— Bishop Be rkeley. The
point he makes is again the difference between two ways of judging
a physical theory: either by its agreement with general principles (the
philosophic criterion) or by the agreement of its consequences with
observations (the scientific criterion). In his book The Analyst, which
is devoted mostly to a criticism of Newton’s doctrine, Berkeley puts
die rhetorical question:

Whether there can be science of the conclusion when there is no evi-
dence of the principle? And whether a man can have evidence of the prin-
ciples without understanding them? And therefore whether the mathe-
maticians of the present age act like men of science in taking so much more
pains to apply their principles than to understand them?

This sounds like a twentieth-century philosopher criticizing Ein-
stein. It may perhaps be objected that Berkeley was not competent to
pass judgment on a scientist like Newton. However, a man like
Leibniz , equally competent as scientist and philosopher, considered
both Newton’s law of inertia an d his law oLgravit ation philosophica lly
false and even absurd.

Two traits in these laws seemed to be incompatible with the es-
tablished principles of philosophy. According to Newton a moving

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disagreement between scientists and philosophers

body keeps its with re spect to the emp ty space. This was

regarded as absurd. How could the empty space exert any action?
Moreover, the law of gravitation assumed that material bodies at-
tracted each other at any distance and instantaneously. This action at
a distance was incompatible with Aristotelian philosophy as well as
with the “mechanisti c” and "geometr ic" philosophy of Democritus or
Descartes. For a material body could only be set in motion by contact
with a second body, bv push or pul l.

Newton himself did not believe that his force of attraction was a
causal explanation of the motion of planets. He expected always to
find a derivation of these laws from general principles which were
connected with a medium exerting an impact upon the planets. He
compared himself to a man who could explain the operation of a piece
of clockwork. Such a man can describe the mechanism by which the fall
of a weight is transformed into the motion of the hands. But if you ask
such a man how the weight manages to fall he would be at a loss.
Nonetheless, you are forced to admit that he has given you a better
understanding of the clockwork than you had before.

This attitude is defined in Newton’s famous dictum, “Hypotheses
non jingo— I don’t set up hypotheses.” This word has been frequently
misinterpreted. For from our present viewpoint Newton’s law of gravi-
tation is a hypothesis too. Newton disappointed his most ardent fol-
lowers in the question of the action at a distan ce as .well as in the
question of the corpuscular theory of light. He was always convinced
that this theory was not the negation of the undulatory theory but
would have to incorporate some elements of the latter. In short, New-
ton was not a faithful Newtonian.

The great success of Newton’s physics was based upon the wide
range of observable facts embraced and by the simplicity and ele-
gance of the mathematical methods employed. It was justified by its
consequences, or, to speak in the language of the Middle Ages, by its
mathematical truth. But the "p hilosop hic trut h” of Newton’s principles
was regarded as very doubtful by his contemporaries. Not only “pure”
philosophers but scientists also passed the judgments that these prin-
ciples were obscure or even absurd.

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modern science and its philosophy

But presently the confirmation of these principles by the increasing
range of physical facts that could be derived from them changed the
attitude of the philosophers too. If we examine the general opinion
toward the end of the eighteenth century we notice a complete revolu-
tion. The law of inertia and the law of gravitation were no longer re-
garded as absurd; on the contrary, they were declared more and more
to be self-evident, derivable fronLpure_reason, the only way in which
the human mind can understand nature.

As an example of this changed attitude we can point to Immanuel
Kant’.ijJ 'Metapbysical Elements of Natural Science,” which was pub-
lished in 1786. We find in this book all the theorems of Newton’s Mathe-
matical Principles of Natural Philosophy, but they are transformed,
so to speak, into a petrified state. Newton had invented bold generaliza-
tions in order to cover a large range of facts that had formerly defied all
at ^atinpgj apprnaeVi All of these general Statements, which
seemed to Newton’s contemporaries so new, so amazing, so absurd, are
now quoted as self-evident. Kant claimed to have demonstrated that
the law of inertia can be derived from pure reason; he claimed that
the recognition of that law is the only assumption under which nature
is conceivable to human reason.

One may say that this was merely the opinion of a philosopher who
was a product of the German inclination toward a foggy metaphysics.
But when we look at the great advocates of empirical p h iloso phy in
the nineteenth century we find almost the same opinion. We may
choose as an example the British champion of .empirical and m echa-
nis tic philoso phy in the middle of the nineteenth century, Herbert
Spence r. In his standard work, Synthetic Philosophy, he expresses him-
self about the law of inertia. He says:

This law means t hat motion like m auer jg This inde-

structibility is not inductively inferred, but is a necessity of thought. For
destructibility catmot be conceived at all ... it is a pseudo-idea. To say
that something can become nothing would establish a relation between two
terms of which one (nothing) is absent from consciousness, which is im-
possible.

This was written in 1860.

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* disagreement between scientists and philosophers

But we may leave the philosophers and examine the attitude of
the scientists of that period. We soon notice that their attitude is
strongly influenced by the success claimed by the philosophers. The
scientists wouJd not exactly say that Newton’s principles of mechanics
could be derived from pure reason, but they would fervently proclaim
that no physical theory is satisfactory which fails to prove that the
observed phenomena are derivable from Newtons laws. Without this
proof no theory could be regarded as a real step toward the under-
standing of nature. I quote two striking examples. About the middle
of the nineteenth century, in 1847, Helmholtz published his famous
paper, “On the Conservation of Energy.” ^ He was a great physicist who
was also a great physiologist and psychologist. He said:

The task of physical science is finally to reduce all phenomena of nature
to forces of attraction and repulsion the intensity of which is dependent
only upon the mutual distance of material bodies. Only if this problem is
solved are we sure that nature is conceivable.

Perhaps still more impressive are the statements of the well-known
physiologist Du Bois-Reymond. He gave, in 1872, an address “On the
Limitations of Natural Science.” This speech was widely discussed in
the last quarter of the nineteenth century. Du Bois-Reymond said:

The cognition of nature is the reduction of changes in the material world
to the motions of atoms, acted upon by central forces, independent of time
... It is a psychological fact of experience that wherever such a reduction
is successfully carried through our need for causality feels satisfied for the
time being.

Is this not an amazing fact in the history of human mind? As New-
ton set up his theory the introduction of the central forces of attraction
was regarded as a particularly weak point of this theory. It was accused
of requiring the introduction of an element that is philosophically
absurd. But what happened about a hundred years later? It was claimed
as a “psychologic fact” that just the same thing— the reduction of a
group of phenomena to the action of central forces— satisfies our need
for causal understanding. And the derivation of physical theorems from

^H. von Helmholtz, Vber die Erhaltung der Kraft (Berlin, 1847).

213

modern science and its philosophy

the action of these forces, which were formerly condemned as un-
conceivable, was now the guarantee that nature is conceivable.

What is the point of all these considerations? By examining the
changes in the appreciation of Newton’s laws we are able to find out
and to understand the origin and the for mation of established phi lo-
sophic princi ples. Both the law of inertia and the law of gravitation
originated as physical hypotheses that enabled the physicist to describe
and predict a large group of observable phenomena in a very con-
venient way. These laws were justified by the success of this enterprise
—that is to say, by their effects— but they could not be recognized as
compatible witli established philosophic principles. They were, if we
apply the language of the Church in its struggle against Copernicus,
^“philosophically false” and merely “mathematically true.”

But what was the situation in the middle of the nineteenth century?
Now, the same laws, the law ofjR^ti^^weUas the law of gravitation,
became themselves established philo sophic p rinciples, with which all
physical theorems had to be in agreement. A physical theorem was now
by definitionJ^hilosQphicaUyJbrue” if it could be derived from Newton’s
laws. We understand now very well that these “established philosophic
'^principles” are nothing else than physical hypotheses in a state of
petrifaction.

It may be asked why we should call it ‘^petrifaction.” A physical
theory can be changed when new facts are discovered that are not
embraced by this theory in a convenient way. But a philosophic prin-
ciple which is derived from pure reason can rigyer be changed or even
modified. I£ Kant and Sp5ncer_are right, that the principle of inertia
can be demonstrated by purely mental operations, no future discovery
of new physical phenomena can bring about any modification of this
principle. The transformation of a physical hypothesis into a philo-
sophic principle is therefore a petrifaction of that hypothesis.

And now it seems very plausible that the philosophic principles of
earlier periods are of the same origin, ^ristode’s principles of physics
were originally also generalizations that covered in a convenient way
a certain group of observed facts. When Copernicus and Galileo ad-
vanced their new physical theories they were declared to be “philo-

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disagreement between scientists and philosophers

sophically false.” This meant only that they were in contradiction with
the petrifactions of Aristotelian physics.

In the same way we can now understand the widespread claim that
the theory of relativity and the quantum theory are valuable des crin-
tions of observed facts but give us neit her a causal u nderstanding nor
a description of phy sical reality. To put it briefly, they are taxed with
being only mathematically true.4)ut-philosDphically_ialse or even
absurd. This means in this case only that they are in contradiction with
the petrifactions of Newton 's_ physi cs. Or in other words, in twentieth-
century physics we are confronted with new experimental facts and
have to change the hypotheses of Newton’s physics. This is possible
as long as these hypotheses are not petrified. But once Newton’s laws
are regarded as phil osop hic principles.which.can b e deduced from pur e
reason they can n o longe r -be- changed. Now every modification of
Newton’s laws will be "philosophically false.”

But knowing the origin of philosophic principles we need not be
terrorized by the verdict "philosophically false.” It means only that the
new physical laws are in contradiction.with ihLe. old ph ysical law s which
appear now disguised as philosophic principles with pretensions of
eternal validity. The old physical theory was a good description of a
restricted group of facts. But to cover the new facts the old theory
became inconvenient. It is natural to drop it, if an obsolete physical
theory does not pretend to be an “eternal philosophy."

This very simple state of affairs has often been described by the
pretentious term “crisis of physics,” or even "cris is of scienc e.”

And now we can answer with a few words the question put in the
title of this chapter. Why do philosophers and scientists so often dis-
agree about the merit a ha new theory ? They mostly disagree because
the new theory seems to be in contradiction to established philosophic
principles. Moreover— and this is my chief point— this disagreement
arises from necessity, for the established philosophic principles are
mostly petrifactions of physical theories that are no longer appropriate
to embrace the facts of our actual physical experience.

.2J5

CHAPTER

the philosophic meaning of the Copernican revolution

I N 1543, four hundred years ago, Copernicus died. This year was in a
certain sense also the year of the birth of the Copernican system.
His great book, “The Revolutions of the Celestian Bodies,”^ was
published in the same year. When this book was published, nearly
fifty years had passed since Columbus discovered America. This event
was one of Copernicus’ starting points. He refers in one of the first
pages of his book to this discovery as the final proof of the spherical
shape of the earth. (Incidentally, he does not mention Columbus and
says, as a matter of course, that “America is named after her dis-
coverer.”) The earth was now definitely a globe, and, to speak in terms
of today, “global thinking” could begin.

To understand a phenomenon means to interpret our present ex-
perience as the repetition of a similar phenomenon of the past. This is
true in science, but it is true as well in history. Today, we understand
the French Revolution better than our parents did because we are
contemporaries of the Russian revolution, and we understand the
Copernican r&voluHnn better than nineteenth-century scientists did
because we are contemporaries of the Einsteinian revo lution.

Let us formulate the central problem of all philosophy of science in
the simplest possible terms. We have to face two worlds: on one hand,
that of our sensg_£)hseml3eaG, sudi as, in astronomy, the observed
^ De BevoluHonlbus OrbUm Celestium.

philosophic meaning of the Copernican revolution

positions of the stars in the sky; on the other hand, that of the general
prinHpT^F such as the law of gravitation and the principle

of relativity. To what extent are these general principles justified by
those sense observations?

This sounds simple enough, but to appreciate the immense gap be-
tween these two worlds means to start grasping the central problem of
all philosophy of science. Unfortunately, the pedagogic effort of science
teachers has been often directed towards camouflaging this gap. If,
however, the very goal of science teaching is to help the students in
the understanding of nature, the actual depth and width of that gap
^must be emphasized over and over again. The state of mind acquired
by the average student of science as the result of inadequate training
has been largely responsible for the failure to appreciate exactly the
philnsapbie-meaning of the Copernican revolution.

Only recently, under the violent impact of twentieth-century
physics, particularly the theory of relativity, have the eyes of science
students been opened and has the meaning of the Copernican revolu-
tion become clear.

If we look into a typical textbook or listen to an average teacher,
we learn that before Copernicus, men believed in the testimony of their
senses, which told them that our earth is at rest, that the planet Jupiter
traverses in twelve years a closed orbit on the celestial sphere and that
this curve contains twelve loops. Finally, Copernicus recognized the
fallacy of this testimony and proved that “in reality" our earth is in
motion and that the planet Jupiter traverses “in reality” a smooth circle
around the sun as center. Copernicus exposed the illusions of our
^nses. Human reason thus scored a clear victory in its struggle against

This description of Copernicus’ achievement seems to me, con-
servatively speaking, inadequate. The loops traced by the planets are
by no means a sort of optical illusion and neither is the immobility of
the earth. As a matter of fact, the planet Jupiter actually traverses every
year a loop with respect to a system of reference that participates in
' the annual revolution of the earth. But the same Jupiter traverses just
as truly every twelve years a smooth circle with respect to the system of

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modern science and its philosophy

fixed stars. Neither the loops nor the smooth circle are results of our
naive sense experience. They are two different diagrams representing
one and the same set of sense observations. Therefore, the interpreta-
tion of Copernicus’ achievement as a victory of abstract reason over
naive sense experience is hardly justifiable.

However, we meet occasionally a second interpretation which say?
almost the opposite of the first one. The hard facts of our sense ex-
perience became more and more incompatible with medieval phi-
losophy, which had its roots in speculative reasoning rather than in
sense observation. Copernicus finally decided to overtlirow the obsolete
doctrines of Aristotle and Ptolemy and scored a victory for experience
in its struggle against pure speculation. As a matter of fact, Copernicus
was not particularly “tough minded,” if we may use the famous phrase
of William James to describe the empirical scientist as distinct from
the "tender-minded” believer in pure reasoning. No new facts had been
discovered by Copernicus, which had forced him to abandon the
geocentric doctrine. The astronomical tables calculated from the
Copernican system were in no better agreement with the observed
positions of the stars than the previous tables.

Therefore we have to start from the fact that the Copernican revolu-
tion meant neither a victory of reason over the illusion of our senses
nor a victory of hard facts over pure speculation. To be sure, Coper-
nicus invented a new pattern of description for our observations. His
genius manifests itself in the beautiful simplicity of this pattern: he
replaced loops by concentric circles.

Copernicus died in 1543. The Roman Holy Office did not utter an
oflBcial judgment on the Copernican system until 1616, seventy-three
years after Copernicus’ death. This Roman verdict will give us the
best hint about the philosophic meaning of the Copernican revolution.
For the verdict considered specifically the philosophic merit of the
new system. The Copernican theory was called “pliilnsophicaily foolish
and absurd .”

But not even Copernicus’ greatest opponents ever doubted that his
system meant a great advance in astronomy. The general opinion in
these quarters was that the heliocentric system is “astronomically true,”

philosophic meaning of the Copernicon revolution

or as it was sometimes phrased, “mathematically true,” but in any case
“philosophically false” or even “absurd.”

We have to do here with a conflict between two conceptions of
truth. This conflict has existed through the ages and has created quite
often a great confusion of mind. This double meaning of truth has never
been dramatized so clearly as by the Copernican revolution and its
repercussions. To understand and to evaluate this conflict is the great
lesson we can learn from the history of the Copernican ideas.

The medieval philosopher St. Thomas Aquinas described very
distinctly two different criteria of truth:

There are two ways to prove the truth of an assertion. The first way con-
sists in proving the truth of a principle from which this assertion follows
logically. In this way, one proves in physics the uniformity of the motion of
the celestial spheres. The second way consists not in proving a principle
from which our assertion can be derived but in assuming our assertion
tentatively and in deriving results from it which can be compared with our
^Observations. In this way one derives, in astrology, the consequences of the
hypothesis of eccentrics or epicycles concerning the motion of celestial
bodies. However, we cannot conclude in this way that the same assumptions
cannot be derived, perhaps, from a different hypothesis also.*

If a statement of astronomy met only the second criterion, the
agreement with observed facts, it was termed “mathematically true.”
Only if it met also the first criterion, that is, if it could be derived from
an evident principle, was it recognized to be “philosophically true.”
Since Aristotle’s physics was supposed to be derived from evident
principles, to be philosophically true meant practically to be in agree-
ment with Aristotelian physics.

As Copernicus had been anxious lest his system might not be
philosophically true in this, sense, he feared some hostility on the part
of theologians who were strict believers i n Aristotelian phi losophy. He
looked for advice on how to behave in this situation, and strange as it
may seem to us, the Catholic churchman Copernicus asked a Lutheran
theologian from Nuremberg how to avoid trouble. The Nuremberg
scholar, Osiander, answered him in a letter of 1541:

* Summa Theologlae,

219

modern science and its philosophy

As for my part, I have always felt about hypotheses that they are not
articles of faith but bases of calculation. Even if they are false, it does not
matter much provided that they describe the observed phenomena cor-
rectly ... It would, therefore, be an excellent thing for you to play up a
little this point in your preface. For you would appease in this way Aristo-
telians and theologians, the opposition of whom you fear.

This advice meant precisely tliat Copernicus should not claim
“philosophic truth” for his system but should be satisfied with a claim
for “mathematical truth.”

But Copernicus did not like this compromise. He claimed his system
to be at least as philosophically true as the Ptolemaic system, and per-
haps even more so. In this way a conflict flared up, the issue of which
was a very subtle distinction. Was the Copemican doctrine a true
description of the universe or was it merely an hypothesis which served
for calculating the positions of the stars? And how did Copernicus
himself look upon this question? Most of the scientists of today are
accustomed to regard every theory as a working hypothesis only, and
would hardly be prepared to give serious thought to that subtle dis-
tinction which is rather an issue of the philosophy of science. But if we
go a little deeper into the logical structure of science, we have to
recognize that, as a matter of fact, every scientific theory, of whatever
period, had to meet the two requirements of a “true theory” which were
already familiar to Thomas Aquinas. In reality, no theory was accepted
merely because it was a good working hypothesis. In every period of
the history of science a theory had to be in agreement with the general
principles of physics. The physicists of the nineteenth century would
hardly have admitted a theory that was in disagreement with the
principle of conservation of energy.

For that reason, practically every theory has been a compromise
between these two requirements. This is particularly true of the
Ptolemaic system. We read and hear frequently that the Ptolemaic
system was in agreement with the Aristotelian philosophy and physics.
But Copernicus, we are told, disturbed this harmony and advanced a
theory that would contradict explicitly the laws of medieval physics.
This was certainly not the opinion of the medieval philosophers them-

220

philosophic meaning of the Copernicon revolution

selves. One of the basic principles of medieval physics was the law that
terrestrial bodies move in rectilinear paths toward or away from the
earth while celestial bodies move in circular orbits with the earth
as center, but the Ptolemaic system assumes that sun and planets
traverse eccentric circles or epicycles the center of which is not the
earth. Therefore, the Ptolemaic system could not be regarded as philo-
sophically true, but at most as a hypothesis that might serve as a basis
of calculation.

Thomas Aquinas judged the Ptolemaic system as follows:

The assumptions made by the astronomers are not necessarily true.
Although these hypotheses seem to be in agreement with the observed phe-
nomena we must not claim that they are true. Perhaps one could explain the
observed motion of the celestial bodies in a different way which has not been
discovered up to this time.

The twelfth-century Arabian philosopher Averroes and his school
emphasized very strictly the philosophical criterion of truth and de-
clined to ascribe any truth value to the Ptolemaic system. Says Averroes:

The astronomers start from the assumption that these [eccentric or
epicyclic] orbits exist. From this assumption they derive results that are in
agreement with our sense observations. But they have not proved by any
means that the presuppositions from which they started are, in turn, neces-
sary causes of these observations. In this case, only the observed results are
known but the principles themselves are unknown, for the principles cannot
be logically derived from the results. Therefore new research work is neces-
sary in order to find the “true” astronomy, which can be derived from the
true principles of physics. As a matter of fact, today there is no astronomy
at all, and what we' call astronomy is in agreement with our computations
but not with the physical reality.

The common opinion among philosophers was rather that the
true picture nf the universe cann ot he discovered by the astronomer,
who is restricted to finding out what hypotheses are in agreement with
observed facts. If different hypotheses meet this requirement, science
cannot decide which is true and, as the Jewish medieval philosopher
Moses Maimonides puts it:

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modern science and its philosophy

Man knows only these poor mathematical theories about the heavens,
and only God knows the real motions of the heavens and their causes.

It is certain, therefore, that before the Copemican revolution no
theory of the motions of the celestial bodies existed that would meet
both criteria of truth. There was in every theory a discrepancy between
mathematical and philosophic truth. Against this background we have
to interpret the famous dedication letter which Copernicus published
as a preface to his great book and in which he recommended his work
to the good will of Pope Paul III.

Copernicus affirms that he did not advance his new theory of the
motions of the heavens in a spirit of opposition against the established
doctrine. His only motive was his conviction that there was no es-
tablished doctrine. The hypothesis of a circular motion of planets
around the earth as center did not account for the observed facts, and
the hypotheses of eccentrics or epicycles were not in agreement with
the general principles of physics which required uniform circular mo-
tions around the earth as center. Since no doctrine existed which could
be regarded as “true” from the philosophic as well as from the mathe-
matical angle, Copernicus felt free to suggest a new hypothesis assum-
ing the mobility of the earth.

This hypothesis accounted for the observed motions nearly as well
as the Ptolemaic theory of epicycles, but removed some of the epicycles.
The motions of the planets became now circular orbits around the sun
as center, except for the epicycles which were necessary to account for
the inequalities in the motion of planets. In any case there were fewer
epicycles and more homocentric orbits in the Copemican, than in the
Ptolemaic, system. Therefore Copernicus claimed that his theory was in
some sense nearer to the requirements of Aristotelian physics than was
the geocentric system. The Ptolemaic system was a compromise be-
tween the two criteria of truth. Copernicus claimed that his system was
in the same sense a compromise and, as he believed, a better one.

In any case, Copernicus claimed to give in his theory a true picture
of the universe, true in every sense of the word. By a strange coinci-
dence. Copernicus’ book was edited by the same Osiander of Nurem-
berg whose advice Copernicus did not like to follow. We understand

«. C

222

philosophic meaning of the Copernicon revolution

now the famous words of the editor s preface, which had been originally
ascribed to the author himself but which reflect only the editor’s
opinion;

The hypotheses of this book are not necessarily true or even probable.
Only one thing matters. They must lead by computation to results that are
in agreement with the observed phenomena.

While Copernicus tried to achieve the compromise by arguing that
his theory is to a large extent in agreement with the principles of
Aristotelian phy sics. Galileo Galilei, in his famous Dialogue on the
Copernican and Ptolemaic Systems of the World, went a good deal
further in the overthrow of medieval science. He no longer attempted
to reach the compromise by adjusting his working hypotheses to the
requirements of the established principles of physics. On the contrary,
he ventured to adjust the principles of physics to the best suitable work-
ing hypotheses. This meant dropping the bulk o f Aristotelian phy sics
and starting a movement in science that led in time to the philosophy
of science which we would call toda y positivism or pragma tism. The
two criteria of truth which were for medieval thinkers like St. Thomas
Aquinas two distinct requirements, have fused more and more into
one single requirement: to derive the best description of the observed
phenomena from the simplest possible principles, while these principles
are justified solely by the fact that they permit this derivation.

Galileo’s ideas were not brought into a coherent system of proposi-
tions until Tsaao Nswtn n advanced his celebrated laws of motion in his
Mathematical Principles of Natural Philosophy. This book appeared in
1687, approximately 150 years after the popemican rfivnlujjnrL. From
the Newtonian principles the Gopemican doctrines could be logically
derived. Therefore, to the believer in these principles, the Gopemican
system was now true in the full sense of the word, philosophically and
mathematically true.

Let us now ask. What did the Gopemican hypothesis look like when
it was derived from the Newtonian principles? It said that the earth
is rotating with respect to absolute space and that the planet Jupiter
traverses smooth circular orbits with respect to absolute space. But

223

modern science and Hs philosophy

Newton himself was very well aware that “motion relative to absolute
space” has, to use P. W. Bridgman's term, no operational meaning,
that is, that by no physical experiment can the speed of a body in
recb'linear motion with respect to al»olute space be measured.

Therefore, the Newtonian system of principles is not a logically
coherent system within the domain of physics. Newton himself restored
logical coherence by enlarging his system of physical statements by
the addition of some theologic propositions. As we read in Burtt’s book
on the Metaphysical Foundations of Modem Physical Science;

CertaiiJy, at least God must know whether any given motion is absolute
or relative. The divine consciousness furnishes the ultimate center of refer-
ence for absolute motion. Moreover the animism in Newton’s conception of
force plays a part in the premises of the position. Cod is the ultimate origina-
tor of motion. Thus real or absolute motion in the last analysis is the ex-
penditure of divine energy. Whenever the divine intelligence is cognizant
of such an expenditure the motion so added to the system of the world must
be absolute.

Under the influence of the spirit of the eighteenth century the
mixing of theology into science began to be regarded as illegitimate.
Strange as it may seem, by the abandonment of theologic argument the
Newtonian physics lost logical coherence. Burtt says very correctly:

When in the twentieth century Newton’s conception of the world was
gradually shorn of its religious relations, the ultimate justification for ab-
solute space and time as he had portrayed them disappeared and the entities
were left empty.

Therefore the new principles of physics from which the Copemican
theory could be derived were far from being satisfactory. The “philo-
sophic truth” of the Copemican system was still a doubtful thing.

Toward the end of the nineteenth century, F.mst Mach exposed
very specifically the logical incoherency of tha Nfiwtonign
as a purely physical system. He claimed on good grounds that the
principles from which the Copemican syste m was derived are es-
sentially thenlngic nr meta physical princip les. Mach claimed in the
nineteenth century, as Averroes had done in die period of the Ptole -

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philosophic meaning of the Copemican revolution

nasaiLsystem, that we have no true astronomy, if “true” means “derived
from a coherent system of principles of physics.” ^

Mach asked for the remo val of the concept of absolute space- from
physics and for a new physics which contains only terms which have
within physics, to speak again with Bridgman, operatiopal

This program, however, was not carried out until Einstein created
his general theory of relativity and gravitation between 1911 and 1915.
This theory, as a matter of fact, was the first system o f-purely physica l
p rinciples from whirh the Cn pemioan system of planetary motions
could be derived. But the description of these motions looked now very
diEerent from the way it had looked as derived from Newton’s prin-
ciples. The concept of absolute space was no longer present. There-
fore the statement of the rotation of the earth and of the smooth circular
orbits of the planets had now to be formulated quite differently.

From Einstein’s principles one could derive the description of the
motions of celestial bodies rel ative tn any -system of reference. One
could demonstrate that the description of the motion of planets becomes
particularly simple if one uses the system of fixed stars as a system of
reference, but there was still no objection to using the earth as system
of reference. In this case, one obtains a description in which the earth
is at rest and the fixed stars are in a rotational motion. What appears
to be in the Copemican heliocentric system the centrifugal force of the
rotating earth becomes in the geocentric system a gravitational effect
of the rotating fixed stars upon the earth,

The Copemican system became for the first time in its history not
only mathematically but also philosophically tm e. But at the same
moment the geocentric system became philosophically tme, also. The
system of reference had lost all philosophic meaning. For each astro-
nomical problem, one had to pick the system of reference that rendered
the simplest description of the motions of the celestial bodies involved.

The reception of the Einsteinian revolution by the scientists of the
twentieth century reminds us in many respects of the reception of the
Copemican revolution by the scientists of the sixteenth century. This
comparison might help us to understand the philosophical meaning
of both.

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modern science and its philosophy

We may take as an example the way in which Einstein deals with
the contraction of moving bodies in the direction of their motion. The
verdict of quite a few twentieth-century physicists was: the theory of
relativity permits us to derive the observed phenomena from hypo-
thetical principles but it does not give a physical explanation of the
contraction. This was an exact repetition of the Roman verdict against
the Copemican system. For the meaning was: the theory of relativity
may be “mathematically true” but it is certainly “philosophically false.”
Now “philosophically false” meant not to be in agreement with New-
- ^tons principles of phy sics, while in the sixteenth century the same
expression meant not to be in agreement with Aristotle’s physics and
Scholastic philosophy.

But what are the facts affirmed by the Copemican doctrine which
are still accepted today as true? Copernicus enthusiastically proclaimed
the sun as the center of the universe and said:

In the center of the Universe the sun has its residence. Who could locate
this lamp in this beautiful temple in a different or better place than in the
center wherefrom it can illuminate the whole of it simultaneously?

Even if we restrict the meaning of the word “universe” to our
galactic system, the Milky W av, this universe is not spherical and the
sun is not located in the center. It has been known for a long time
that our galactic system has the shape of a lens. Before the distance of
very remote stars could be estimated, it was plausible to believe that
our sun, with our earth as attendant, is located in the center of this lens.
However, in the twentieth century new methods were developed for
estimating the great distances of remote stars, in large part by Harlow
Shapley and his collaborators of the Harvard Observatory. In par-
ticular, Shapley found that our sun is not located near the center of
that lens, but approximately 30,000 light years away from it. This
means that the sun with our planetary system is near the edge of the
lens. According to Copernicus, we inhabitants of the earth have no
longer the great satisfaction of being the center of the universe, but we
have at least the small satisfaction of being the attendant of a master
who has his residence at this center. But according to Shapley, man

philosophic meaning of the Copernican revolution

has lost all reasons for complacency. He is not even the attendant of a
master who occupies the central stage of the universe.

Copernicus probably believed that the orbits of celestial bodies can
be described in the best and simplest way by taking the sun as a body
of reference. In our twentieth century, we know that this caimot be
true universally. According to Einstein s theory of gravitation, there is
no "all-purpose system of refere nce.” Copernicus’ suggestion of using
the sun is practical only if we restrict ourselves to the motions in our
planetary system. For eve ry particular purpose a particular svsten i'
may be the most suitable.

Copernicus did not discover any new fact that could be regarded as
established for all eternity. But he denied to the earth its former role
as the only legitimate body of reference, he demonstrated that the sun
is the most suitable system for a particular purpose, and he cleared
the way for the great new truth that we have complere fr^pdrYm in,f> iir
choice of a system of reference.

The Copernican revolution did not end by replacing the earth as
master of the Universe by the sun or by absolute space, but it was only
the first step in a series of revolutions that culminated, so far as we
know today, in depictin g a de"i »<^»-aHr» nrriar nf the universe in which
all celestial bodies play an equal part.

227

CHAPTER

the place of the philosophy of science in the curriculum
of the physics student

I F we wish to exercise sound judgment about the success or failure of
science teaching in the general scheme of our educational system,
it may be a good idea to arrange a hearing. We may then listen to
people who were compelled to submit to this teaching and later
achieved such a great reputation in om cultural life that we cannot
ignore their opinions about the contribution of science teaching to
general education.

Ralph Waldo Emerson, who complained that science had become
abstract and remote from human life, says in his essay on Beauty in
“The Conduct of Life”:

The formulas of science are like the papers in your pocketbook, of no
value to any but the owner . . . There’s a revenge for this inhumanity.
What manner of man does science make? The boy is not attracted. He says,
I do not wish to be such a kind of man as my professor is.

If the goal of a teacher is to stimulate, by his own example, en-
thusiasm for his subject, Emerson s teachers of science seem not to have
come very near this goal. It may be that Emerson was not a science-
minded type. We may quote, therefore, a recent writer, who, besides
his wide interests in all domains of human life, had a particular leaning
toward science— H. G. Wells. He describes bis reaction to his physics

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philosophy of science in the physics curriculum

teachers in the Normal School of Science in London. He realizes exactly
that what is wrong is not the ability of a particular teacher. “No man,”
says Wells, "can be a good teacher when his subject becomes inexpli-
cable.” He amplifies this statement:

To a certain point it had all been plain sailing, a pretty science, with
pretty subdivisions: optics, acoustics, electricity and magnetism, and so on.
Up to that point, the time-honored terms which have been ciystaUized out
in language about space, speed, force, and so forth sufficed to carry what I
was learning. All went well in the customary space-time framework. Then
things became difficult. I realize now that it wasn’t simply that neither
Guthrie nor Boys was a good teacher . . . The truth, of which I had no
inkling then, was that beyond what were (and are) the empirical practical
truths of the conservation of energy, the indestructibility of matter and force,
and so forth, hung an enigmatic fog. A material and experimental meta-
physics was reached . .

H. G. Wells indeed laid a finger on a very sore spot in our science
teaching. The "subject has become inexplicable” because the teachers
themselves did net have traming that pat the emphi^sis oa logical eon-
sistency and satisfactory coherence between abstract law and sensory
observation. Their upbringing was a purely technical one, with little
regard for the role of science within our culture as a whole. Where
physics teaching reached a domain beyond mechanical and electrical
engineering, the subject was not satisfactorily explained because it was
“inexplicable.”

There is no doubt that the current interest in science has its origin
not only in its technical application, but also in its bearing on our gen-
eral world picture. Our generation is witness to the “relativity boom.”
At the peak of this boom, Einstein’s theory was of hardly any use to
the engineer. But, to express it perfunctorily, it changed our view
about the “nature of time and space.” The statement that conciurently
with a given event here a certain event is occurring on the planet
Mars, was formerly taken to have a definite meaning. We know now
that such a statement can only be asserted “relative to a certain sys-
tem of reference.” This new doctrine appeared to add credit to the

'■H. G. Wells, Experiment In Autobiography (New York: Macmillan, 1934),
pp. 175”

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modern science and its philosophy

doctrine of the “relativity of truth” and seemed therefore to some
people a “social danger,” since it might contribute to a disbelief in the
“absolute values” of ethics.

These problems have been haunting our generation for decades.
But if we ask a trained physicist (not to speak of a graduate engineer)
what his opinion is on these questions, we notice immediately that
his training in physics has not provided him with any balanced judg-
ment. The scientist will, as a matter of fact, often be more helpless than
an intelligent reader of popular science magazines. We face the same
situation if we ask our graduate in physics whether the theory of
quanta has justified the belief in the freedom of will or whether it has
made a contribution toward the reconciliation between science and
religion, as has been maintained frequently, even by scientists and phi-
losophers of high reputation.

The great majority of these trained physicists— and by "majority”
I mean more than 90 percent— will be unable to give any but the most
superficial answer. And even this superficial answer will not be the
result of their professional training, but the profit they have made from
reading some popular articles in newspapers or periodicals. As a mat-
ter of fact, most of them will not even be able to give a superficial an-
swer, but will just say, “This is not my field, and that’s all there is to it.”

The result of conventional science teaching has not been a critically
minded type of scientist, but just the opposite. The longing for the
integration of knowledge is very deeply rooted in the human mind.
If it is not cultivated by the science teacher, it will look for other out-
lets. The thirsty student takes his spiritual drink where it is offered to
him. If he is lucky, he gets his information from popular magazines or
science columns in newspapers. But it can be worse, and he may be-
come a victim of people who interpret recent physics in the service of
some pet ideology which has been, in quite a few cases, an anti-
scientific ideology. The physical theories of the twentieth century have
been interpreted, indeed, as having “abandoned rational thinking”
in favor of— I don’t know exactly what, as I cannot imagine what al-
ternative exists to rational thinking in the field of science.

It is a fact which one may regret, but which is established em-

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philosophy of science in the physics curriculum

pirically with no less certainty than the law of gravitation, that the
science student who has received tlie traditional purely technical in-
struction in his field is extremely gullible when he is faced with
pseudophilosophic and pseudoreligious interpretations that fill some-
how the gap left by his science courses. I would even venture the
statement that this gullibility increases in inverse proportion to the
familiarity of the student with the conceptual analysis of science. I
think that, statistically, the experimental physicist is more gullible
than the theoretical physicist, and the graduate of an engineering
school still more so.

For our purpose, it is suflBcient to realize that the present type of
science instruction does not enable the student to form even the faint-
est judgment about the interpretation of recent physics as a part of a
new world picture. This failure prevents the science graduate from
playing in our cultural and public life the great part that is assigned
to him by the ever-mounting technical importance of science to human
society. It is obvious that the necessity of teaching twentieth-century
physics has made conspicuous the shortcomings in our methods of
science teaching. It would be erroneous, however, to think that the
teaching of earlier, so-called classical, physics is not handicapped by
the same kind of shortcoming. But, certainly, these deficiencies be-
come the more conspicuous the more rapid the changes in physics
that have to be presented in class.

If we look, for example, at the treatment of the Copemican con-
flict in an average textbook of science, we notice immediately that the
presentation is far from satisfactory. In almost every case, we are told
that according to the testimony of our senses the sun seems to move
around the earth. Then we are instructed that Copernicus has taught us
to distrust this testimony and to look for truth in our reasoning rather
than in our immediate sense experience. This presentation is, to say
the least, very misleading. Actually, our sense observation shows only
that in the morning the distance between horizon and sun is increas-
ing, but it does not tell us whether the sun is ascending or the horizon
is descending. Starting from this fundamental mistake, the average text-
book does not provide the student with an adequate picture of the

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modern science and its philosophy

historic fight of the Roman Church against the Copemican system. The
student does not leam the way in which a powerful organization can
oppose a doctrine established by science, and how this opposition can
muster the support of reasonable and bright persons like the father of
British empirical philosophy, Francis Bacon, who denounced the Coper-
nican system as violating our common sense.

By its failure to give an adequate presentation of this historic dis-
pute our traditional physics teaching misses an opportunity to foster
in the student an understanding of the relations between science, reli-
gion and government which is so helpful for his adjustment in our
modem social life. With a good understanding of the Copemican and
similar conflicts, the student of science would have even an inside
track in the understanding of social and political problems. He would
be put at least on an equal level with the student of the humanities.

Let us now proceed with our hearing: having listened to Emerson
and Wells, let us question an intelligent college student who is not a
concentrator in science but who has taken, say, a beginning course in
chemistry or biology to round out his general education. We shall hear
often of a deep dissatisfaction with these science courses as a contribu-
tion to general education. While such a student may carry away from
his courses in history or literature the impression that they have guided
him into a wide-open field of human interest with an outlook in a great
many new directions, he has had a very different reaction to his science
courses.

We may take our example from the chemistry classes, where, ac-
cording to an old tradition, the general outlook is more neglected than
in the other sciences. In such courses, where science teaching is at its
worst from the educational angle, formulas like HgSO^ are thrown upon
the head of the student, and he will really feel, as Emerson did, that
these formulas are “notes in a pocketbook, which are valuable only to
the owner”— who is, in this case, the professional chemist— but without
any broad human interest. The general student will get the impres-
sion that he sits in a show where formulas are tossed around in a kind of
juggling game. This is, of course, a very inadequate impression, but
one to which the student will inevitably be led by the purely tech-

philosophy of science in the physics curriculum

nical approach in the teaching. He will probably not be much im-
pressed if he is told that this juggling leads eventually to interesting
results, perhaps in the field of solid and liquid fuels. For “fuel” is, after
all, no broad human interest either, but obviously a concern for some
specialists.

If, however, chemistry should be taught in a more human way, it
would be clear that a formula like H2SO4 contains the history of man-
kind, the evolution of the human mind in a much more impressive and
certainly more condensed way than does all the history of the British
kings. What a good teaching of science has to achieve on behalf of
general education is to bring out the heroic mental efforts of man-
kind, which are packed in the formula H2SO4 as in a nutshell, and to
let the student live through the exciting historical and psychological
experience that eventually found its abridged expression in such a
formula. Then the “note in a pocketbook” will become a flamin g mani-
festo to mankind.

The foregoing discussion raises serious doubts as to the ability of the
traditional method of science teaching in fitting science into the broader
framework of human knowledge. For the scientist himself this state of
affairs may be satisfactory or at least tolerable, provided that the
student gets a good understanding of his own field, say physics. But
I am afraid that the same shortcomings that have in the past been ob-
stacles to fitting physics into a broader frame of reference may also
be obstacles in the path leading to a satisfactory understanding of
physics itself.

In order to check this apprehension, we have only to put to a
student of science the following simple question, which is, in a cer-
tain way, a key question: What does it mean when you say that a
geometric theorem— for example, the sum of the angles in a plane
triangle is equal to two right angles— is “true”? The significance of this
question was emphasized with the advent of non-Euclidean geometry.
Even in a perfunctory treatment of non-Euclidean geometry the ques-
tion will arise: What does it mean to say that our actual space is
Euclidean or non-Euclidean? This question was regarded as very

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modern science and its philosophy

natural and pertinent by the founders of non-Euclidean geometry. It
was, actually, a very common question when this new geometry was
a novelty. But if, today, you examine a graduate in mathematics or
physics, the majority will never have heard of such a question, and if
you put it to them they will not understand its meaning without a very
thorough interpretation. If we look into any current textbook of non-
Euclidean geometry, which may have several hundred pages, hardly
half a page will be devoted to the question of “truth,” and these few
lines are mostly an attempt to dodge the question. In most cases, the
student will not even learn such a simple thing as that mathematics can
prove only statements of the type: if theorem A is true, then theorem
B is also true; but it can never prove whether A is true or not.

This failure of science teaching in the foundations of geometry has
a devastating effect on the mind of the student. For if he does not
grasp the exact relationship between mathematics and physics in this
simplest example offered by geometry, later he will certainly be unable
to understand precisely the relation between experimental confirmation
and mathematical proof in the more involved domains of physics or, for
that matter, in any exact science. This means that he is bound to mis-
understand altogether the role of mathematical theory in physics. The
failure of a satisfactory elucidation in such a fundamental matter has
made it possible to find in a well-known textbook of college physics
statements like this; Einstein proved “mathematically” that a material
body cannot move with the speed of light. The student of physics
is not even trained to get the instinctive feeling that no statement of
physics can be proved mathematically, but that every "proof’ in physics
consists only in deriving mathematically one physical fact from other
statements about physical facts.

By the failure to give a good account of the exact relation be-
tween mathematical proof and experimental confirmation, our tradi-
tional science teaching again misses an opportunity to teach the student
a reasonable and scientific approach to all problems of human interest.
For in all these fields the central problem is the relationship between
sensory experience (often called fact finding), and the logical conclu-
sions that can be drawn from it. The failure to grasp exactly the nature

philosophy of science In the physics curriculum

of this relationship accounts for the confused attitude of many people
toward the complex problems by which they are faced in private and
public life.

The role of mathematics and physics in the understanding of geom-
etry is perhaps the simplest example by which the student can learn
how to discern the role of facts and logical conclusions in the involved
problems of human relations. As a matter of fact, every problem of
physics where mathematics is applied gives us such an example. A
simple and typical example is provided by Newton’s laws of motion.
The first law (law of inertia) and the second law look very simple,
but they are a crucial issue for every instructor who teaches physics to
beginners. Their apparent simplicity makes it easy to discover every
confusion in the presentation, whereas in the treatment of an advanced
subject of mechanics, such as the problem of three bodies in celestial
mechanics, a little confusion can pass unnoticed.

It is not an exaggeration to say that 90 percent of the textbooks
of physics on the college level present the law of inertia in such a way
that its meaning is obscure; it is formulated in words that are not ap-
plicable to any actual situation in the physical world. We learn mostly
that a body upon which no force is acting is “moving along a straight
line.” But obviously the expression “moving along a straight line” has
a physical meaning only if a system of reference is physically given,
in which a straight line is fixed that serves as the model by which we
judge whether a certain motion is rectilinear or not. But in the current
textbooks of college physics one finds hardly even the perfunctory
statements that the system of reference needed in the first law is the
system of the so-called fixed stars. Hence, the statement of the law as
it occurs in the textbooks has not even a vague meaning, for no method
is described by which the validity of the law can be tested in a con-
crete case.

Since the method of testing remains obscure, one finds all imag-
inable opinions regarding the possibility and method of testing the
validity of the law of inertia. In some books one reads that the law is
self-evident and does not need any empirical proof; other authors,
however, say that it is confirmed by the most familiar experience of

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modern science and its philosophy

our daily life; for example, a book lies quietly ou a table if it is not
taken off. Tills, again, is in contradiction to the assertion of some
textbooks that the law of inertia is a hypothesis that cannot be proved
by any experiment

If one seeks an evaluation of this law of inertia as an achievement
of the human mind, one finds not infrequently such statements as: it
is ama zing that it took so many centuries to discover such a simple
and trivial law. It does not occur to these authors that this law may,
after all, not be so "simple” as they believe, if so many great scien-
tists were unable to discover it earlier. Obviously, to call it “simple
and self-evident” means not to understand its real significance and
not to give to the students a correct presentation.

While in the elementary textbooks the law of inertia is formulated
in an elaborate but mostly meaningless way, many advanced textbooks
take pride in minimizing the law. I even found a book in this category
in which the law of inertia is called “self-explanatory.” The author
himself fails to explain it, relying evidently on the ability of the law
to explain itself. In these advanced books the law of inertia is treated
as a special case of the second law: acceleration is proportional to
force. If the force is zero, the acceleration obviously is zero too, and the
body moves with constant velocity. But the only distinction between
this and what the elementary books say is very often that in the ad-
vanced book not the first, but the second law is formulated in a mean-
ingless way. The result can be easily checked, if we ask any graduate
student in physics what the word “acceleration” in the second law
means. He will certainly know that the acceleration is the second
derivative of the coordinates with respect to time; but when we ask
him what is meant exactly by "coordinates,” he will say that they refer
to a Cartesian coordinate system. But a motion of a physical body is
described only if we specify its coordinates with respect to a co-
ordinate system that consists of physical bodies at which we can point.
Therefore, to give an “operational” definition of what is meant by
“acceleration” in the second law, we have to describe a particular
physical Cartesian system. This certainly must not be in fixed con-
nection with our earth. In the first approximation, we can take the

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philosophy of science in the physics curriculum

body of fixed stars, our Milky Way, as such a Cartesian system. Then
acceleration is, approximately, “acceleration with respect to our Milky
Way.” Most students of physics will be at a loss if asked a simple
question like this. Even a candidate in the Ph.D. examination will some-
times answer that "acceleration” in the second law means “accelera-
tion with respect to a Cartesian system the axes of which are fixed in
space.” Many will not even have a vague apprehension that the ex-
pression “fixed in space” may be meaningless in physics. But if one
asks them a little more insistently, they will become confused and
will guess that there is something rotten in their knowledge of the
simplest laws of physics.

This failure to describe the physical system of reference to which
Newtons laws refer does not do any harm to the student who takes
mechanics for its use in mechanical engineering. For in this restricted
domain he can work on the assumption that our own earth is the
system of reference that is meant in the definition of “acceleration.”
In the extreme case, he will have to resort only to the system of fixed
stars, as in computing the influence of the rotation of the earth on the
orbit of a launched projectile. The engineer who has never heard of
the difficult problem involved in the expression “acceleration” in New-
ton’s law will by this failure not imperil the lives of people who use a
bridge that was built according to his computations.

Obviously this state of happy innocence becomes obnoxious if it is
preserved in the treatment of cosmological problems. The fixed stars,
of course, are not at rest with respect to one another and do not ex-
actly form a rigid Cartesian system. Therefore, they cannot be sub-
stituted in the Newtonian laws for the abstract term “Cartesian sys-
tem.” Rather, we must say that the positions and velocities of the fixed
stars, and even of the remote nebulas, determine in some way the
system of reference that the Newtonians mean when they use the term
“acceleration” without any specifications. This means that the motion
of a rolling billiard ball on earth is physically influenced by the posi-
tions and velocities of our Milky Way, and even by the galaxies that
are millions of light years away from the earth. They determine the
motion that we call “motion under no force.” By ignoring the influence

modern science and its philosophy

of the large but remote masses of the universe, the mysterious concept
of “absolute space” was introduced into science. It remained there as a
heritage of an ancient state of science which later was interpreted as
metaphysics.

Obviously, as in the case of geometry, by the failure to give a satis-
factory presentation of Newton’s laws the teaching of physics misses a
valuable opportunity. It could give to the student an example of the
elimination of concepts that are leftovers from an earlier state of sci-
ence and have survived in the disguise of metaphysical concepts. The
“absolute space” and the “Cartesian system without physical back-
ground” can be proved to be superfluous for any logical derivation of
observable fact. The student understands easily that they have no
legitimate status in science, and are only the source of an odd verbiage
about "real motions” in contrast to “apparent motions.”

In the sciences that deal with human behavior the situation is es-
sentially the same. One makes use of expressions like “real freedom”
in contrast to “pseudofreedom,” but the muddle around these expres-
sions is very hard to disentangle. To learn how “real motion” was elim-
inated from science is a very good example of how to proceed in other
fields. Hence, it has an educational value that can hardly be over-
estimated. It paves the way for a correct analysis in the social sci-
ences. But we are not to restate this issue of value for general educa-
tion in this section. Rather, we shall stress the point that the same short-
comings which make the traditional presentation of Newton’s laws
unfit for general education, bar also its use for the understanding of
physics itself, particularly of recent physics.

It is a fact which can hardly be overlooked that in the average
college curriculum little attention has been paid to the theory of
relativity compared with the great interest which this theory has met
among the general public, and compared with the bearing of this
doctrine on atomic and nuclear physics, not to speak of its key role in
the logic of science. When, for example, the theory of the electro-
magnetic field is treated in the regular college curriculum, there are
many teachers who skip the relation to the theory of relativity or treat
it perfunctorily. They will tell the student that “relativity” is an obscure

philosophy of science in the physics curriculum

theory which the student would hardly understand. By treating the
subject in tliis perfunctory way lliey certainly contribute to the
obscurity that may prevail in the mind of the student. He becomes
convinced that the theory of relativity is fundamentally different from
“sound” physics, such as Newtonian mechanics or Maxwell’s electro-
magnetic field. He is likely to believe that modem theories are less
logical and less closely related to the observed facts. The origin of this
attitude must be found, certainly, in the insufficient training of teachers
in the field of relativity. As a matter of fact, there is even a shortage of
appropriate textbooks. There are good textbooks on relativity for ad-
vanced students and there are fairly good books for laymen, but a book
on this subject for the undergraduate hardly exists.

It is easy to put the finger on the gap in the training of college
teachers which produces their antipathy to a thorough treatment of
relativity theory in the regular physics courses. The lack of precision
in the foundations of geometry and mechanics at which we pointed
does no harm in mechanical engineering, but becomes a major danger
when we have to teach relativity. To the mechanical engineer the
whole problem of the system of reference is trivial. He can get along
splendidly with our good old earth as such a system. But when we
go in for more general problems, such as motion with great speed,
propagation of light, and so forth, we have to keep in mind constantly
that these phenomena can be described with respect to different sys-
tems of reference. For some particular changes of the system of ref-
erence the laws of motion remain unaltered. This fact turns out to be
the most important property of these laws, and is the very basis of the
theory of relativity.

If the teacher fails to stress the role of the system of reference in
ordinary mechanics, the student will later fail to grasp the gist of the
theory of relativity. Moreover, if words like “absolute space” or "ab-
solute rest in space” are not eliminated by adequate teaching of me-
chanics, the student will have trouble eliminating the concepts of
“absolute length” or “absolute time” in relativity. Frequently, the teach-
ing of traditional college mechanics has not been used to give to the
student a correct understanding of the relation between mathematics

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modern science and its philosophy

and observation in science, but instead the metaphysical formulation of
Newton’s laws is hammered into the student’s brain, as is done in most
textbooks. Then the study of the theory of relativity will be a hard
job for instructors and students. They will easily wind up in the pit-
falls of metaphysical prejudices which are mostly covered by a thin
stratum of common sense. They will believe that expressions like “ab-
solute simultaneity” or “absolute length of a time interval” are im-
mediately understandable to common sense. The result is, of course,
that these students, on becoming instructors in physics, will never be
able to get rid of the opinion that the theory of relativity is somehow
contrary to common sense, or, at least, not as agreeable to it as tra-
ditional physics has been.

This situation is still worse in the approach to the quantum the-
ory. As this theory is badly needed to organize experimental results in
atomic physics, it would be hard to eliminate the quantum theory
from the regular physics curriculum. But the teachers who do not feel
on firm ground in the foundations of geometry and mechanics will
teach the quantum theory as a collection of useful recipes, “quantiza-
tion laws,” which often take the form of “prohibitions.” They will dodge
as much as possible the new general laws that have replaced the New-
tonian science. The student will get little of Heisenberg’s principle of
indeterminacy or Bohr’s principle of complementarity, which are the
most relevant points in quantum theory for our general world picture.
And if these points are touched, the same thing will happen as in the
ordinary treatment of relativity. The student will be left with the
impression that the new physics is somehow obscure and even “irra-
tional.” This perfunctory presentation of the new principles is, in some
respects, even worse than the practice of restricting the teaching pre-
cisely to the formulas that describe actual observations. For the feel-
ing that science has to be satisfied with an obscure theory makes the
student an easy victim of quacks who exploit modem science in their
endeavor to prove that we have to surrender our reason to a kind of
blind instinct. This means in practice that we have to surrender our
good judgment to the control of people who are bold enough to pre-
tend that they are in possession of that intuitive instinct.

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philosophy of science in Hie physics curriculum

To summarize these remarks: if the teacher of science takes it easy
in the presentation of the foundations of geometry and mechanics, the
consequences of this carelessness will leave imprints on the minds of
the student that will make it very hard to train him later as a teacher
of modem physics.

H. G. Wells, in his criticism of the science teaching he went
through, says very correctly:

The science of physics is even more tantalizing today above the level of
elementary introduction (optics, acoustics, etc.). Brilliant investigators
rocket o£E into mathematical pyrotechnics and return to common sense with
statements that are, according to the legitimate meanings of words, non-
sensical. Ordinary language ought not to be misused in tliis way.

This statement gives a good diagnosis of the disease by describing
it as basically a “semantic maladjustment,” as the school of general
semantics would call it today. “Clearly,” Wells continues, “these mathe-
matical physicists have not made the real words yet, the necessary
words that they can transmit a meaning with and make the basis of
fresh advances.” As we shall see in the next section, these words even
hint at the remedy of the illness.

We have shown that our traditional way of teaching science is re-
sponsible for two deficiencies in the education of our students. First,
not all instmctors in science are up to the role that science, particularly
physics, has to play in our general cultural life. Second, the twentieth-
century theories (relativity and quantum theory) are still an obscure
domain outside the well-illuminated field of common-sense physics.
Uneasiness has not been removed by our usual teaching of physics.

If we now put the question of how to improve this situation, we
know from the preceding discussion the sources from which the failure
of our traditional teaching has originated. We know how it has hap-
pened that our science instruction is not successful in fitting science
into our cultural life, and the modem theories into the frame of
common-sense physics.

We discovered the main source in the failure to teach the students
a clear distinction between the observation of facts and the drawing of

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modern science and its philosophy

logical conclusions. David Hume, the father of empiricist philosophy,
has urged us to “surrender to the flames” all books that contain neither
observed facts nor mathematical conclusions. This recommendation
has become the basis of all attempts to make science a coherent and
empirically confirmed system of knowledge. Accordingly, we have to
teach our students how to eliminate all statements that are neither
propositions describing the result of an observation, nor propositions
that are part of a logical conclusion.

Therefore, we have to insist, above all, that the student leam to
analyze the statements of his science in such a way that it becomes
obvious what is a statement of observation and what is a logical con-
clusion. Many statements made in the traditional presentations of
physics, particularly of recent theories, do not belong to either of the
two types.

If we have carried out this analysis, it is convenient to present the
result in such a way that from the wording of every statement it imme-
diately becomes clear what its logical status is. For, in the traditional
presentation of science, we are often unable to recognize whether a
given statement is meant to be a statement about observed facts, or a
hypothesis about facts that will be observed, or a statement that merely
introduces new words or rules for construction of propositions. This
distinction, however, is necessary.

If we try to single out the purely logical statements, we find them
in every science. In geometry, for instance, a great part of scientific
work consists in deriving conclusions from a given set of propositions
called axioms. In drawing these conclusions, we do not need to know
what the words in the axioms mean in the physical world. If the
“points” and “straight lines” and “triangles” have the properties that
are ascribed to them in the axioms, they also have the properties that
are ascribed to them in the theorems, which we obtain by logical con-
clusions from the axioms. In the same way, in mechanics, if we start
from Newton’s equations, ma — f and a = d“x/dt®, we can derive, by
logical conclusion, a great many theorems. We find that if the force is
zero, the coordinate x is a linear function of time, and if the force is con-
stant, the coordinate x is a quadratic function of time, and so on. These

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philosophy of science in Ae physics curriculum

statements are true whatever the meaning of “force f or “coordinate at”
or “time t“ may be in the physical world.

We obtain in this way purely logical statements. One occasionally
calls them “tautological statements” because they tell us only that one
and the same assertion can be expressed in diflFerent ways. If ma = f
and f = 0, it follows that x is a linear function of t. But from this con-
clusion we do not learn anything about the physical world; we learn
only to say one thing in different ways. By this perfunctory hint we
learn already that more than a few failures in our customary science
teaching have originated in the failure to recognize clearly the tauto-
logical character of these statements.

The world of physical experiments— briefly, the “physical world”
—is described by statements about the procedure and results of physical
measurements. They boil down, eventually, to statements like "a
certain colored spot covers a second colored spot,” or statements about
a “pointer reading,” as Eddington calls it. They consist only of words
that are familiar to everybody. The description of physical experi-
ments does not contain any element that is not used in describing our
breakfast, and is therefore understandable to everybody who is trained
to use the English language in his daily life. These statements have,
obviously, a certain vagueness, and they are never completely un-
ambiguous.

These “observational statements” are the second type of statement
that we can single out in any science. In geometry, for example, we
show how to measure the angles of a triangle and can And that the
sum of the results is approximately 180°. In mechanics we measure the
distance of a body from the floor of a room, and can find that in the
case of a launched ball the distance from the floor is approximately
a quadratic function of the angle traversed by the hand of a clock.

These two types of statements, the logical and the observational,
contain different types of word. In the first one, we have symbols like
“points” or “forces” or “coordinates,” which have no meaning at all in
the physical world, while the second type contains words of our
‘Tdtchen language,” which denote familiar things of our environment.

Customarily, the student learns in science classes that by observa-

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modern science and its philosophy

tional statements it is possible to confirm or refute the axioms of geom-
etry or laws of mechanics. But, obviously, this way of speaking is some-
what superficial and logically incorrect. For the “observational
statements” contain words of everyday life like “green,” “hard,” “over-
lapping spots,” and so forth, while the “axioms of geometry and me-
chanics” contain symbols like “point,” “circle,” “acceleration,” “force.”
A statement of the second type can never be confirmed or refuted
^ by a statement of the first type, because it does not contain the same
terms.

If science consisted only of principles and observations, its validity
could not be tested by scientific methods. It is, therefore, of the utmost
importance to teach the student that, besides these two types of state-
ment, science has to make use of a third type by which the language
of the abstract principle can be translated into the language of obser-
vation. If the principles contain, for example, the word “length,” one
has to describe the physical operations by which the length can be
measured. As these operations can be formulated in the language of
everyday life, of observational statements, the description of the oper-
ation translates the abstract term “length” into terms of observational
language.

These translating sentences have been studied with particular em-
phasis and care by F. W. Bridgman, and are called, according to his
suggestion, “operational definitions.” By this definition, an abstract
term like ‘length” acquires “operational meaning.” When these “oper-
ational definitions” are introduced into the abstract principles, the lat- '
ter become “observational statements.” Then we can check by actual
experiments whether these observational statements, derived from the
principle, check with the observational statements that describe our
direct physical experiments. It is necessary to understand that only in
this indirect way can the principles of science be checked by experience.

Nowadays, the term “semantics” is often used to denote the study
of the relation between words and meaning. Hence, the sentences by
which symbols are coordinated with observable things are called
“semantic rules.” They occur in die writings on the logic of science
under different names. F. S. C. Northrop uses them as “epistemological

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philosophy of science in the physics curriculum

correlations,” H. Reichenbach as “rules of coordination,” and so on.

This “logico-empirical analysis,” or “semantic analysis,” is a general
method of “making our ideas clear.” It is an eflBcient method for com-
munication of thoughts and for influencing people. This analysis is the
chief subject that we have to teach to science students, in order to fill
all the gaps left by traditional science teaching.

If the student were taught this method effectively, he would be
able to present and to understand recent physical theories— like rela-
tivity and the quantum theory— as precisely as classical physics, if—
and this is the great “if”— if he understands ordinary geometry and
mechanics precisely. Therefore, as charity should start at home, so
semantic analysis should start in our own scientific back yard, at the
foundations of our familiar geometry and mechanics. The application
of logico-empirical analysis was never presented so clearly and con-
cisely as in Einstein’s paper, “Geometry and Experience.” He sum-
marizes the results by saying; As far as geometry is certain, it does
not tell us anything about the physical world, and as far as it makes
statements that can be tested by experience it is not certain— that is
to say, not more certain than any statement of physical science. By
operational definitions "straight lines” can be translated into “light
rays” or “edges of rigid bodies.” Then the theorems of geometry be- .
come statements of optics or mechanics. Without these definitions, all
(porems of geometry are tautological propositions about symbols,
ticsioreover, if we apply this type of analysis to mechanics, we shall
1 step Uv ask: what is the operational meaning of “acceleration”? If
we wfiil aii< translate this symbol into an expression consisting of ob-
servational terms, we have to describe the physical system of reference
to which the coordinate x refers.

If we apply the same method to the theory of relativity, this doc-
trine will lose its isolated and obscure character. It will be obvious that
“length” or “simultaneity” have to be defined by the description of
physical operations by which these quantities can actually be meas-
ured. If yardsticks and clocks are affected by motion, it is equally
obvious that the operational definitions of spatial or temporal ‘length”
have to contain the velocity of the yardstick or clock relative to a physi-

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modem science and its philosophy

cal system of reference. This means that only “relative length” has an
operational meaning, not "absolute length.”

The reason why the theory of relativity has appeared so obscure
to the physicists will then be very clearly understood by the student.
Every alteration of the laws of physics seems understandable to com-
mon sense, if the semantic rules are unaltered. This would be the case
if we replaced the wave theory of light by the corpuscular theory, pro-
vided both theories remain within the frame of Newtonian mechanics.
But the experiments on bodies moving with great speed suggest the
introduction of new semantic rules. Such a change is much more funda-
mental and will appear obscure to the student of physics, if he is not,
from the start, taught the role of these semantic rules in every do-
main of science, beginning with his high school plane geometry.

Bridgman rightly stresses the point that for a student who has
studied relativity successfully, there is no need for a subsequent intro-
duction to logico-empirical analysis. He could not understand relativity
without it. The instruction in the two theories is inseparable.

In a similar way, if we apply this analysis to the quantum theory,
no student would fall for the talk that there is some “irrational” or
“organismic” aspect in the quantum theory. He would understand that
the very meaning of Bohr’s principle of complementarity can be defined
as the introduction of new semantic rules into the language of physics.
As the alterations required by these rules are much more radical thct
those required by the relativity theory, the confusion of languag per-
been tremendous. As our traditional teaching fails often to me lat- .
correct logico-empirical analysis, a great many author. ■ by and
philosophers alike— have failed to recognize that we have to ao with a
radical alteration of semantic rules. Many of them have even been
caught by a widespread propaganda by which the new physics of the
twentieth century has been exploited in die service of a campaign
against the spirit of science, in favor of a confused “organicism,” “spir-
itualism” or “irrationalism.”

Clearly, by learning the application of semantic analysis, the stu-
dent will not only profit from a better understanding of his own science,
but also gain a more correct appreciation of the role his science plays

philosophy of science in the physics curriculum

in the frame of human culture in general. The close relationship of
semantic analysis to modem physical theories on the one hand, and to
the understanding of our general social and cultural life on the other
hand, has perhaps nowhere been stressed so bluntly and sharply as by
Bridgman, in a paper published in 1945.' He discerns the technical and
the semantic significance of twentieth-century science, when he says:

The second aspect of the modem epoch in science is, I believe, of in-
comparably greater significance ... He [the physicist] has come out with
what amounts to a new technique of analysis, of great power and unexpect-
edly wide range of applicability. The new technique is applicable to all ques-
tions of meaning . . . The potentialities of the new technique, when applied
to domains outside the present application of science, may be glimpsed by
contemplating the confusion which now reigns ... It is becoming evident
to an increasing number of people that an important part of our difiBculties
in analyzing and conveying meaning is of verbal origin . . . There are
popular discussions of semantics.

To appreciate this popular trend toward semantics, we need only
look at such books as Hayakawa’s Language in Action,^ which was a
best seller. In ETC; A Review of General Semantics, edited by Haya-
kawa, semantics is applied to the problem of race relations, to labor
problems, to the psychology of fear, and so forth.

Our point has been tliat an important step toward improvement of
our science teaching could be taken by consistent application of seman-
tics or logico-empirical analysis. I do not believe, however, that this
step would be sufficient. Even if such an analysis is carried out in a
careful and competent way, there still remains much to be done if we
want to bring out all the educational value that is inherent in science.

Once when I explained to a class the second law of Newton by the
method of logico-empirical analysis, stating precisely the operational
meaning of the symbols m, a and f, a student asked: Is this really every-
thing contained in the law? Has die intuitive conception of a “force
acting upon a body,” which has played such a decisive role in the his-

*P. W. Bridgman, Yale Review 34, 444 (1945).

‘ S. I. Hayakawa (Harcourt, Brace, 1941}; also see W. Johnson, People in
Quandaries (Harper, 1946).

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modern science and its philosophy

tory of our thought, completely evaporated into the thin air of logical
rules and physical measurements? As another example, everybody vv^ho
has ever participated in discussions about the principles of physics
occasionally encounters the person who becomes excited when the
question is raised whether the concept of force can be eliminated from
physics. At this point an emotional element enters the debate. The
heat of the argument had its origin certainly not in science itself, but
in the stretch of history of the human mind, which is now packed
into the word “force.” In the time when the Nazi party and its philoso-
phy flourished, we could frequently find in German writing the view
that the concept of “force” is somehow connected with the Nordic race.
All people who wanted to eliminate it from physics were branded as
enemies of the Nordic race. On the other hand, those who plead for the
elimination of the concept of “force” regard it as a remainder of an
animistic and anthropomorphic world picture, which even has a touch
of spiritualism and superstition.

We learn from this example that, in order to understand the role
that the concepts and principles of science have played in our cultural
life, we need, in addition to the semantic, an analysis of a different
type. We have to learn not only the operational meaning of symbols
like “force” and “mass,” but also how it has come about that just these
symbols were chosen. Obviously the choice has not been unambigu-
ously determined by their abihty to form a basis for the derivation of
observable facts. The symbols also have a life of their own. If we go in
for this kind of research, we find that extrascientiflc reasons have been
^ largely responsible for the predilection in favor of or the aversion to
some symbols. We learned it from the example of “force.” A careful
and thorough investigation has shown that psychologic reasons have
played their part, as have habits carried since childhood, and even
wishes emerging from the subconscious.

Besides these factors of individual psychology, the religious, social
and political trends of the period have been responsible for the pre-
dilections and aversions of which we spoke. What we need, therefore,
for an all-round understanding of science is an analysis of the psycho-
logic and sociologic factors that went into the determination of our

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philosophy of science in the physics curriculum

scientific symbolism. We may speak, briefly, of a “socio-psychologic”
analysis. We can summarize and say that this second type of analysis
has to be added to the semantic analysis.^

Both types of analysis are parts of what one calls in more or less
popular discourse “philosophy of science.” Thus we may say that the
remedy for the afore-described shortcomings in our traditional way of
teaching science is to give more attention to the philosophy of science.
More precisely, we mean by it logico-empirical and socio-psychologic
analysis, or, in the terminology of the school of thought known as
logical empiricism: we need semantic analysis and “pragmatic anal-
ysis.”

We have now to attack the more practical question of how the
desirable instruction in the philosophy of science should and could be
given to the students of science.

In my opinion, the best solution is that the elementary science
courses themselves should contain a good deal of the philosophy of
science. This solution presupposes, of course, that there are a sufiBcient
number of science teachers available who have adequate training in
the philosophy of science. Speaking now in terms of what should be,
rather than in terms of what is, I believe that no teacher should give an
introductory course in science if he lacks training in semantics and the
history of science. I realize that this solution is not feasible today.
Hence, my second choice is to introduce courses in the philosophy of
science which are to be obligatory for the students of science, at least
for those who are later to become teachers of science. In a certain way
every scientist is a teacher of science in his environment, whether he
works as an engineer, a physician, or even a pharmacist.

Courses in the philosophy of science for the benefit of science stu-
dents have been given rarely; hence there is no coherent tradition. We
are faced with the problem of building up such a tradition. There are
two reefs that have to be avoided. The greatest weakness of the at-
tempts which have been made occasionally to give such courses has

* Jean Piaget, Les Troit Conditions cTtme iplstdmologle scientipque. Analysis
(Milan, 1940), Vol. 1, No. 8, p. 25.

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modern science and its philosophy

been the lack of any definite conviction on the part of the professor.
We must never forget that the word "professor” is derived from
“profess,” and this holds true, particularly, for a teacher of philosophy.
His work with the students should be a “profession” in both meanings
of this word. Scientists who have been teaching the philosophy of
science have mostly oflFered a kind of incoherent digest of philosophic
opinions. The choice has been mostly determined by the chance ac-
quaintances of the teacher. The students have remained unimpressed
by such courses or books. We meet this eclectic attitude even in the
writings of such excellent scientists as Jeans or Planck. I remember the
lectures of a great physicist, Boltzmann, on the philosophy of physics,
which I attended as a student. Despite the personal greatness of the
lecturer, the effect of the course was slight, because of a lack of a
coherent approach. We can notice, on the other hand, that scientists
who built their books around a central idea have shaped the minds of
science students for decades. I mention, just as examples, Mach,
Poincare and Bridgman.

Although a coherent approach is the first requisite for successful
instruction, the second reef on which our course could be wrecked is a
narrow-minded indoctrination. I remember that an intelligent girl
student told me once: “It is a very unpleasant feeling to have a certain
doctrine drilled into your brain without being provided with an out-
look into the open field of widely divergent opinions.” These two
requirements of a coherent approach and of an open field seem to
exclude each other. But this is true only superficially. If the socio-
psychologic approach is added, it becomes clear that every opinion
which has been advocated in history has its legitimate place within a
coherent presentation of science, based on logico-empirical and socio-
psychological analysis.

Our problem now is, practically, to build a course in which the
student gets training in both types of analysis— a course that not only
fills the gap left by the traditional science teaching, but also leads into
the wide field of controversial ideas for bridging this gap.

For six years I have given a course at Harvard with this goal in
mind. I have tried to improve it from year to year according to my

philosophy of science in the physics curricuium

increasing experience with students. I will describe the content of this
particular course because of my familiarity with it, and not because I
believe that it necessarily represents the best possible course. The
course takes two terms. Actually, I give two half-courses which are
designed for students of diflFerent backgrounds. But in this description
I am going to integrate both half -courses into one coherent presenta-
tion.

My starting point has been the traditional distinction between
“scientific truth” and “philosophic truth.” Specifically, I have referred
to the formulation that the great medieval philosopher, Thomas
Aquinas, gave to this distinction. According to him, there are two
criteria of truth: the first requires that a proposition can be logically
derived from “evident principles” (philosophic truth); the second
requires that the logical sequences of the proposition in question can
be confinned by experience (scientific truth). Obviously, if the truth
of the principles themselves can be tested only by comparing their
logical consequences with experience, the two criteria merge and we
have only one criterion, namely, the scientific one. Then the traditional
distinction disappears. This is the view that is called "empiricism,” or
“positivism.” To assume the distinction obviously means to believe in
principles the truth of which can be checked by extrascientific methods.
In modem science this distinction is no longer upheld as an absolute
distinction, but it has always played a certain role in a weakened and
“relativized” form. We still say that there are propositions of physics
which can be “proved” if we use the traditional language of physics
textbooks. This means that they can be derived from general prin-
ciples (like conservation of energy) which we hold to be true with a
high degree of plausibility. Distinguished from these are propositions
that are records of direct observation and cannot be “proved.”

After these introductory remarks, a historical survey is given of the
principles that have actually been used by the scientists as the basis
from which the propositions of physics have been logically derived.
There is one period in history that we can study from the origin to the
end. This is the period of mechanistic physics, which lasted approxi-
mately from 1600 to 1900. Its basic principles were Newton s laws of

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modern science and its philosophy

motion. A proposition of physics was regarded as “explained,” or
“understood,” or “proved to be true,” if it could be logically derived
from Newton’s laws of motion. But the question arose, of course,
whether Newton’s laws, themselves, were “evident principles.” The
belief that they are arises very often among students of physics as a
result of the perfunctory way in which these laws are presented in the
traditional textbooks. The only effective way to destroy this belief is
to give a thorough presentation of the period before 1600, which pre-
ceded the era of mechanistic physics. In my course, medieval and
Aristotelian physics is presented and analyzed carefully. I call it
“organismic physics,” because the basic principle is the analogy be-
tween physical phenomena and the behavior of organisms.

If the student has become aware that there was a time when reason-
able people did not believe in Newton’s mechanics, it will not con-
travene his “common sense” to learn that after 1900 a period could
start in which these classical laws of motion were modified radically.
Having become familiar with a conception of physics that prevailed
before the period of mechanics, the student will look at the disintegra-
tion of mechanistic physics around 1900 as a phenomenon analogous
to the disintegration of organismic physics around 1600. In both cases,
before the actual revolution took place under the impact of new dis-
coveries of facts, the belief in the certainty of the ruling principles was
shaken from within by logically minded critics. In medieval physics
this role was played by the school of nominalism (Occam’s razor),
while the criticism of mechanistic physics came from the “positivists”
of the last quarter of the nineteenth century, men like Stallo in America
and Mach in central Europe.

The rise of twentieth-century physics, of relativity and the quantum
theory, was closely connected with a new view of the basic principles.
It was no longer taken for granted ffiat the principles from which the
facts had to be derived should contain a specific analogy, either to an
organism or to a mechanism. Nothing was required except that the ^
observed phenomena could be derived from the principles in a con- »
sistent way and as simply as possible. The words and symbols that
occurred in the principles, and the way these were coimected, could

philosophy of science in the physics curriculum

be invented according to their fitness as bases for deriving the phe-
nomena discovered by the experimental physicist.

This means that the symbols used in the principles had in them-
selves no meaning beyond their value for the derivation of facts. From
this introduction of abstract symbols arose the obvious need for in-
cluding in the theory prescriptions for relating these symbols to sense
observations. The necessity and the importance of these sentences were
particularly emphasized and elaborated by Bridgman in his require-
ment of “operational definitions.” This new aspect of physics, which
dismissed any traditional analogy and stressed only the criterion of
empirical confirmation and logical coherence, may be called “logico-
empirical physics.”

Under this name I refer in the course to the physics of the twentieth
century, and dismiss by this terminology aU misleading metaphysical
interpretations of relativity and quantum theory which we owe to phi-
losophers, sociologists, theologians and— I am sorry to say— also to
some physicists.

After this historical framework has been established, I proceed to
the application of logico-empirical analysis to the most relevant parts
of physics. The start is made with geometry, where the situation is
easier to explain than in any other field. I believe that the logico-
empirical analysis of geometry provides the student of science with the
best introduction to the philosophy of science. I would even venture
to say that, if there is little time available, the familiarity of the science
student with the analysis of geometry would suffice to fill, in a fairly
satisfactory way, the gap left by traditional mathematics and physics
teaching. By this analysis the student will learn that mathematics can-
not prove any facts, but can only derive facts from other known facts.
He will learn that there are two fields of science that we call
“geometry.” “Mathematical geometry” has the previously described
tautological character and cannot teach us anything about the “nature
of space.” He will learn that only by the introduction of operational
definitions— for example, “a straight line is a light ray”— can theorems
of geometry become statements about facts and be confirmed experi-
mentally like any law of physics. He will learn that no geometric

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modern science and its philosophy

theorem by itself can be confirmed by experience, but only a geometric
theorem— such as the one about the sum of angles in a triangle— plus
the operational definitions, of straight lines, and so on. He will learn
that statements like "the axioms are self-evident,” or even “they are
true,” are meaningless if no operational meaning is given them.

I would even venture to say that a thorough semantic analysis of
geometry contributes more to the intellectual outlook of the student
than a superficial philosophic interpretation of the whole field of
physics. By this analysis of geometry the student will be introduced to
the new logical techniques in modem physics. Bridgman says of these
techniques that their impact on the pattern of our culture will eventu-
ally be greater than that of the technical consequences of modern
physics, including atomic energy. The logico-empirical analysis of
geometry will, moreover, enable the student to form a sound judgment
about the "tmth” of non- Euclidean geometry, and in this way fill a gap
that yawns in most textbooks. The problem of “tmtli” is usually dodged
in the presentation of non-Euclidean geometry, so that this part of
mathematics has remained obscure to most students.

Then the course passes to the analysis of Newtonian mechanics.
From the beginning, the operational meaning of terms is stressed. This
means, above all, that the role of the system of reference emerges
clearly. Newton’s laws are presented not as self-evident, but as para-
doxical, for so they appeared to Newton’s contemporaries.

We proceed then to the mechanical theory of light. When inter-
action of light propagation with the motion of large material bodies
occurs, and both phenomena are assumed to follow Newton’s laws of
motion, one can predict phenomena that are in contradiction to ob-
served facts, as in Michelson’s experiment.

This contradiction is the origin of the restricted theory of relativity,
which is analyzed thoroughly with the emphasis on the logico-empirical
aspect and on the place of operational definitions. Then all those mis-
understandings disappear that have made this theory “obscure” and
“contradictory” to common sense. It becomes obvious that the role of
the observer is not different from his role in Newton’s physics. No sub-
jective element occurs in physics and, hence, there is no argument in

philosophy of science in the physics curriculum

favor of idealistic philosophy. The revolutionary changes brought about
by relativity consist, first, of new observational facts, such as the change ^
of the rate of clocks by motion, and second, in the suggestion which
Einstein made to alter the language in such a way that these new
phenomena can be described in a simple and practical way. The rela- .
tivily of time, for example, is no advance in metaphysics, but it is in I
physics and semantics.

In the same way the quantum theory is analyzed. The famous rela-
tion of indeterminacy has nothing whatever to do with the introduc-
tion of a subjective or spiritual factor into physics. It is actually a sug-
gestion for introducing a language that best fits the facts. Since there is
no law of physics that incorporates the expression, “the position and
velocity of a small particle at one and the same instant,” there is no
reason to introduce such an expression into the language of physics.
Bohr’s principle of complementarity suggests that our physical world
be described in a complementary language.

The course then proceeds to a logico-empirical analysis of the con-
cepts of causality, determinism, indeterminism, and chance along the
same lines. Eventually the concepts of mass and energy are analyzed.

After this description of the way in which semantic analysis is
actually applied to physics, the course turns to problems of what has
traditionally been called “philosophy.” The first, historical part was a
survey of the way in which principles of science have developed from
the organismic to the mechanistic physics, and further to the logico-
empirical stage. In this stage there was no demand for a specific type
of principle or a specific form of words in the principles. The wording
of the principles became irrelevant from the viewpoint of science itself.
But there have been extrascientific reasons for insisting on principles
of a certain type. These reasons include mere sluggishness in changing
old principles or, very often, theological, ethical, or political factors. It
has been argued that the principles of science have to be in agreement
with the prevailing principles in those extrascientific fields. We re-
member the Thomistic distinction between philosophic and scientific
truth. This distinction is based on the belief that one can assume some
principles for reasons which are not in agreement with their conse-

modern science and its philosophy

quences as experienced. This means that one assumes these principles
for extrascientific reasons. Every system of thought that has this belief
as its basis is a metaphysical system. Since in these systems the prin-
ciples are closely connected with the religious, moral and political
predilections of a certain period, the study of the metaphysical founda-
* tions of science is important for the understanding of the position of
science in our cultural life. Therefore, the next part of the course is
devoted to the metaphysical and antimetaphysical interpretation of
science.

The most important point, as it seems to me, is to get the student to
understand the extremes. I take pains to present an adequate concep-
tion of “straight metaphysics” and, at the other extreme, “straight
positivism,” which bluntly says that there is no principle except those
which can be confirmed by the agreement of their consequences with
experience.

As the example of straight metaphysics, the Thomistic philosophy
is presented at length as far as it serves as a basis of science. The stu-
dents are encouraged to read a textbook of “cosmology” that is cur-
rently used in Catholic colleges and contains the Thomistic founda-
tions of physics. Once I asked a teacher at a Jesuit college, who was
taking my course, to explain to the students the authentic teaching of
Thomistic philosophy.

Then I proceed to the other extreme, which denies the distinction
between the two kinds of truth and recognizes only scientific truth.
I give a short historical survey starting with David Hume, followed by
a short account of A. Comte’s “positive philosophy” and a more elabo-
rate discussion of positivism at the end of the nineteenth century; of the
Americans, Stallo and C. S. Pierce; of the Europeans, Mach and Poin-
care. Passing to the twentieth century, we discuss the “operationism”
of Bridgman and its relation to the pragmatism of William James and
Dewey. Bridgman’s emphasis on the role of language leads us to the last
phase of positivism, the logical positivism of Wittgenstein, Carnap, and
others.

After the presentation of straight metaphysics and positivism, we
^discuss some attempts to produce a reconciliation between the two

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philosophy of science in the physics curriculum

views. There are scientists and philosophers who present science gen-
erally in the positivistic manner, but reserve a jeparate compartment
for metaphysics. Among them are Spencer, Fiske and P. Duhem. Sys-
tematic attempts at reconciliation have been made on the basis of ideal-
ism and materialism. The most powerful idealistic attempt is the school
of thought founded by the German philosopher, Kant. Proponents of
this school claim that there are self-evident principles, but that they are
actually statements about our own minds. By making statements about
geometry, we actually make statements about our own way of de-
scribing nature. Therefore, these statements are, in a certain sense,
checked by experience, but not by external experience. We observe om:-
selves and believe that we observe the external world. An outstanding
representative among the scientists of recent days of this Kantian com-
promise is the British astronomer, Eddington, whose views are dis-
cussed elaborately in the course. There are a great many varieties of
Kantian idealism. They fill the whole spectrum of opinions between
positivism and metaphysics.

The other important scheme of reconciliation is materialism. In its
original form it was a generalization of mechanistic physics, with no
metaphysics in it. Later it became obvious that the phenomena of life
and of human behavior could not be interpreted easily in terms of
Newton’s mechanics. But a great many people felt the relevance of
keeping to the mechanistic scheme. In contrast to mechanistic ma-
terialism, Marx and Engels developed the system of dialectical ma-
terialism, in which “matter” no longer means the matter of mechanics,
but a substance which possesses all the qualities that are needed to
account for the evolution of human life, individual and social. The
importance ascribed to the principles of this system often went beyond
their value for the description of observable phenomena, and the pos-
sibility of any change in these principles was minimized. This attitude
brought a bit of metaphysics into dialectical materialism. After it had
become the official philosophy of the Soviet Union, the relevance of die
principles themselves was bolstered by extrascientific reasons. Dialecti-
cal materialism is discussed in the course in its application to the
foundations of science. As in Kantian idealism, we find in dial^tical

257

modern science and its philosophy

materialism all varieties from almost pure positivism to almost pure
Hegelian metaphysics'. ^

These discussions of the philosophic interpretations of science are y
of great importance to the general education of future scientists. The
interpretations should not be neglected in the teaching of the phi-
losophy of science, for they are the link connecting science with the
humanities. They provide the instrument that is used by religious,
ethical, and political creeds to muster the support of science. F. S. C.
Northrop emphasized in his recent book. The Meeting of East and
West* the great importance of the philosophy of science for any
ethical or political creed. To understand this connection, we have to
understand the philosophic interpretations of science and the link of
metaphysical creeds with religious and political creeds.

The last part of the course is devoted to the description of these ties.

It has become almost a commonplace that the communist and other
left-wing creeds have their philosophic basis in materialism, while the
right-wing groups look for their foundation mostly to some kind of
organismic metaphysics, for example, to Thomism. It is, therefore,
very important that the student have a good training in those philo-
sophic interpretations which have become the bases of political creeds.

I The combination of philosophic and political creeds is often referred
to as “ideology.” The student of science does not need to be ignorant of
this important field. He can take science and its interpretations as his
door of entrance. For this reason, in the course in philosophy of science
much attention should be paid to these philosophic interpretations of
science that have been the basis of ideologies. The most elaborate of
these interpretations are Thomism and dialectical materialism. Prom-
inent cardinals of the Roman Church, as well as prominent political
leaders like Lenin, who were able to look under the surface of things,
have taken pains to introduce into the teaching of science an interpreta-
tion that is favorable to their creed. Hence, the future scientist should
be taught to take advantage of these ties and get a real insight into
historical and contemporary ideologies.

The discussion of these ties helps to make the course in the phl-

* Macmillan, 1946.

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philosophy of science in the physics curriculum

losophy of science relevant and attractive to the student. Moreover,
this way of presenting world problems makes it possible to include a
discussion of the relations between science and religion— a subject often
regarded as too delicate for a sincere presentation, and so either omitted
or presented in a conventional way. On the other hand, I have noticed
that students are extremely interested in this topic, and ask embar-
rassing questions if it is treated evasively. If religion is discussed among
the ideologies, the treatment can become sincere, precise and in-
offensive. It will become clear that in this question also the best way
of approach is from science through its philosophic interpretation.

This is one possible outline of a course on the philosophy of science.
The choice which I made among a great many possibilities is, of course,
determined by my own background, scientific and personal. A great
many paths can lead to the same goal. But all possible courses must, in
my opinion, be based on logico-empirical and socio-psychological an-
alysis of science. Only by this method can we steer our ship between
the two reefs of overspecialization and superficiality.

259

CHAPTER

science teaching and the humanities

1. Special Field and General Education

T here is a widespread belief that the rising contempt for toler-
ance and peace is somehow related to the rising influence of
scientific thought and the declining influence of ethics, religion
and art as guides of human actions. This contention is, of course,
debatable. There is hardly a doubt that the causes of war can be traced
back quite frequently to religious or quasi-religious creeds and very
rarely to the doctrines of science. The humanities, including religion
and ethics, have been for centuries the basis of education and the
result has been, conservatively speaking, no decline in the ferocity of
men. The scientists have never had a chance to shape the minds of
several generations, Therefore, it would be more just to attribute the
failure of our institutions to educate a peace-loving generation to the
failure of ethical and religious leaders than to impute the responsibility
to the scientists,

I do not think, however, that it makes much sense to discuss the
share of responsibility. For I agree wholeheartedly with the critics of
science in the belief that the training of generations of scientists in
mere science, without making them familiar with the world of human
behavior, would be harmful to the cause of civilization. Whether we
like it or not, scientists will participate more and more in the leadership

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science teaching and the humanities

of society in the future. Also there is hardly a doubt by now that the
contribution of the scientists to our political life has been more on the
side of peace and tolerance than have the contributions of the students
of law or government, or, for that matter, of philosophy proper.

In order to make this attitude of our leading scientists a habit
among the rank and file, it is important to imbue the future worker in
science with an interest in human problems during his training period.
Since for this purpose it is futile to argue for the supremacy of human-
istic education over science education, the debate "science versus
humanities” or vice versa is, of course, without point here. But it is
also of little avail to compel the student of science to take some courses
in the departments of humanities. According to the record of all the
people I know, the mentality of the average science student is such that
he will not sufficiently appreciate these courses, and therefore will not
assimilate them well. What we actually need is to bridge the gap be-
tween science and the humanities which has opened and widened more
and more during the nineteenth and twentieth centuries. According to
my opinion, this can be done only by starting from the human values
which are intrinsic in science itself. The instruction in science must
emphasize these values and convince the science students that interest
in humanities is the natural result of a thorough interest in science.

In this way the science teacher will be giving his support to the
whole cause of general education as well as to his specialized teaching
of science.

Everyone who has ever tried to raise his voice for the cause of gen-
eral education among the faculty members of a university has been
running almost regularly against one very definite objection: whatever
of their time the students have to spend in classes on general education
they have to subtract from the time they devote to specialized work in
their own scientific field. As this field is, in any case, so vast that it can-
not be covered during their stay in college, it would be almost a crime
to curtail this short and valuable time. This attitude is particularly
strong among the teachers of science proper.

I am going to discuss the issue “special field versus general educa-
tion" mainly from the viewpoint of science students. However, I am

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modern science and its philosophy

sure that the general picture will be about the same in any other field
of study, in languages, in history, and so on.

Even the departments of philosophy have kept to a policy of isola-
tionism. Instead of working toward a synthesis of human knowledge,
they have proposed a kind of truce between science and philosophy.
In my opinion, this gap is greatly responsible for the rift in our gen-
eral education, or, exactly speaking, the gap between science and phi-
losophy is the most conspicuous part of the gap between science and
the humanities— and hence the gap between science and the realm
of human behavior in general.

This gap is perhaps nowhere so clear-cut and conspicuous as in
the domain of physical science. Therefore, the battle for the renewal
of liberal education will not be won without a willing and intensive
cooperation of workers in the physical sciences. On the other hand, if
we want the students of the humanities to go in g’adly for general
education which requires them to take in quite a few helpings of
science, we must convince them that by learning science they will also
advance toward a better understanding of human behavior.

I am going, first, to describe the harm that the rift between science
and philosophy has done to both of these fields and to the cause of
liberal education in general. Second, I am going to make some sugges-
tions as to how this rift can be repaired by removing the causes
through which philosophy and science have been estranged.

2 . Philosophic Interest In Physics

There is no doubt that the public interest in the physical sciences
is primarily due to their technical applications: television, radar, the
atomic bomb. When Copernicus suggested that the motion of the
celestial bodies be described with respect to the sun rather than with
respect to the earth, this suggestion was quite irrelevant for any
technical purpose. Yet the public interest and the heat of the debates
were certainly greater in this than in the case of any new technical
device. But we need not go back several centuries for examples, since
we ourselves have been witnesses of the “relativity boom” which arose
when Einstein advanced his new theory of motion and light. Although

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science teaching and the humanities

tbis theory seemed at that time very far from any technical application,
the public interest was in some cases rather hysterical, and there are
examples of people who were almost killed in an attempt to get into
an overcrowded lecture room where Einstein in person tried to put over
relativity to his audience. There is also no doubt that the philosophic
and even religious implications of such general physical doctrines ac-
count for the fact that quite a few clergymen have been eager to make
use of relativity in their sermons. In order to appreciate this situation
correctly, we must not forget that Newton, during and after his life-
time, was a popular topic of parlor conversation and that many books
popularizing Newton were published, some of them especially designed
for "the use of the ladies.”

Nowadays we find, not infrequently, books and magazine articles
written by clergymen, philosophers, or, for that matter, by scientists, in
which the theories of modem physics (relativity and quantum theory)
are recommended for their philosophic or religious benefits. We learn
from these papers that twentieth-century physics has restored the
place of mind in the universe, that it has reconciled science with re-
lig on, and that the tide of materialism characteristic of eighteenth- and
nineteenth-century science has definitely been broken in the twentieth
century. As “materialism” has always been connected with some politi-
cal and social systems, these authors conclude that the new physics
means also a defeat of all political systems based on materialism, by
which they mean, according to their personal bias. Communism or, oc-
casionally, Nazism (racism).

There is no doubt that the correlation between physics and phi-
losophy has been largely responsible for the great interest in twentieth-
century physics of wide sections of the general public. The intelligent
reader who follows the trend of contemporary thought in books and
magazines, who listens to popular lectures of scientists, preachers,
philosophers and global politicians, would often have a greater in-
terest in the general ideas of twentieth-century physics than an average
student of physics who specializes, say, in radar. Even after gradua-
tion, a student of physics usually knows very little about the relation
between physics and philosophy, let alone between physics and human

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behavior. He is generally less trained than the educated layman in
forming a well-balanced judgment on such problems as are daily dis-
cussed in magazines and lectures about the influence of modern physics
on human affairs. If a student in high school or, for that matter, in
most colleges, asks his physics teacher for information about problems
of this kind, he will hardly get a satisfactory answer. The information,
if any, will mostly be perfunctory and evasive. Therefore, the graduates
in physics will rarely be able to advise the general public on questions
which this public regards as relevant for their general outlook on man
and the universe.

This failure of the learned physicist will not stifle the public interest.
The thirst for knowledge which is not quenched by the scientists will
be assuaged by people who are ignorant in science but know how to
give answers that flatter the wishes of the majority of people. Thus the
longing for knowledge of large sections of the public will become grist
for the mills of some organized propaganda groups.

The textbooks of physics mostly claim to stick to the facts and to
exclude “idle philosophic talk.” But actually, they formulate the gen-
eral laws of nature often in such a way that no physical facts whatso-
ever can be logically derived from these laws. This means that they
really formulate not physical but purely metaphysical laws.

Thus, the physical sciences provide very good examples from which
students can learn that the expression “sticking to the facts only” is
frequently used as a pretext for avoiding all logical analysis, and there-
fore for favoring all kinds of obsolete prejudices. What one should
reasonably mean by "sticking to the facts only” is to make only state-
ments that can be checked by experience, that is, by observable facts.
This habit is certainly of great use in debunking empty slogans and
bigotry in politics or religion.

As “sticking to the facts” is the slogan of traditional physics teach-
ing, “ignoring the facts” is a slogan cultivated in the traditional teach-
ing of mathematics. Both these slogans are logically legitimate within
a restricted domain of thought. However, on occasion, the students
have to learn the limitations of these slogans; otherwise, the meaning
of the most important laws of nature cannot be made clear to them.

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science teaching and the humanities

and the very goal of general education on the basis of science would
be frustrated.

3. Chance Phlloiophles

Without an understanding of the tie-in between mathematics and
physics, the student misses the best opportunity of grasping the most
important trait of human knowledge: the relation between sense ob-
servation and logical thinking. If this bridge between the fields is not
built by a thorough analysis of the empirical and logical procedure in
science, that is, by a systematic philosophy of science, the necessity for
it is so overwhelming that it will be built anyway. This will be done
mainly by some obsolete but popular philosophy which will replace
the thoroughly logical analysis of science. It is noteworthy that, in
practice, crude empiricism in science, without critical analysis, has
often made possible the fiourishing of crude metaphysical systems.

Quite a few great thinkers who belonged to very divergent schools
of thought have been unanimous on one point; if a scientist believes
that he has no philosophy and keeps tightly to his special field he will
really become an adherent of some “chance philosophy,” as A. N.
Whitehead puts it. This great contemporary metaphysician with a solid
scientific background assures us that for a scientist deliberately to
neglect philosophy

is to assume the correctness of the chance philosophic prejudices imbibed
from a nurse or a schoolmaster or current modes of expression.

We find complete agreement with this opinion in a statement of
Ernst Mach, a philosopher and eminent scientist who was the most
radical enemy of all kinds of metaphysics. He says, about obsolete
doctrines of philosophers, that they “have survived, occasionally, much
longer within science where they did not meet such an attentive criti-
cism. As a species of animals which has been badly adjusted to the
struggle of life has survived sometimes, on a remote island where there
have been no enemies, obsolete philosophy has survived within the
borders of science.”

As a third and again very different type of thinker we may quote

265

modern science and its philosophy

Friedrich Engels, the lifelong collaborator of Karl Marx, who was par-
ticularly interested in the consequences of obsolete philosophy in social
and political life. He says:

Natural scientists may adopt whatever attitude they please, they will
still be under the domination of philosophy. It is only a question whether
they want to be dominated by a bad fashionable philosophy or by a form
of theoretical thought which rests on acquaintance with the history of
thought and its achievements

One thing seems to be certain: if we try to eliminate from, say,
physics, all teaching of the philosophy of science, the result will be not
a crop of scientifically minded physicists, but a flock of believers in
some fashionable or obsolete chance philosophy.

Among science students, the students of engineering are those who
get traditionally the worst training in philosophic analysis. They often
absorb science, stripped of its logical structure, as a mere collection of
useful recipes. Is it only a coincidence that the students of engineering
have on the whole been more impressed by empty political slogans
(like Fascism) than the students of “pure” science? There is no doubt
that general slogans play a role in politics s'milar to the role that gen-
eral principles play in science. If someone is trained to understand
to what degree general principles like conservation of energy or rela-
tivity are based on confirmable facts and how far on arbitrariness and
imagination, he is more immune to the political slogans of demagogues
than a student who has been trained only to record his immediate ex-
perience and to regard the general laws as gifts dropped from heaven
for helping him to bring some order into his record sheet.

Practically, the separation between science and philosophy can be
kept up strictly only during a period in which no essential changes in
the principles of science take place. In a period of revolutionary
changes the walls of separation break down. In Whitehead’s statement
quoted above, he makes particularly the point that the lack of phi-
losophy of physics among the physicists may be harmless in a time of
stability, but during a period of reformation of ideas this lack will lead

^F. Engels, Dialectics of Nature, English translation by C. Dutt (New York:
International Publishers, 1940), p. 243.

science teaching and the humanities

unavoidably to the chance philosophy of which we spoke. Our own
age, with the rise of relativity theory and quantum theory, is an obvious
example. These new fields have actually become, not only for the lay-
man but also for the physicist of average training, a kind of mystery.

Different methods have been used by physics teachers to dodge the
issue of giving to their students a coherent picture of the laws of nature.
The simplest thing to do is to stick as closely as possible to the descrip-
tion of physical devices and the presentation of mathematical computa-
tions. This way of teaching has given the nonphysicist the impression
that the science of physics, which has been, historically, the spearhead
of enlightenment, has become in some cases a source of obscurantism.
Quite frequently physics has actually been used to attack belief in
human reason and to bolster belief in irrational sources of truth. This
misuse had its basis certainly in the failure of many books and instruc-
tors to give a logically consistent interpretation of the physical meaning
of the formulas that express the most general laws.

4, "Profatsional Philoiophy"

Besides the departments of the special sciences there is in most
colleges a department of philosophy, which is to counteract the ex-
treme specialization. It is devoted to the task of investigating the
foundations that are common to all the special sciences. According to
our previous argument, the average instruction in the special sciences
has not achieved the goal of giving to the student an understanding of
the place of his science in the whole of human knowledge and human
life. Let us now inquire how the average instruction in philosophy has
done the job which has been ignored by the instruction in the special
sciences. As a matter of fact, philosophy (as taught in most depart-
ments of philosophy) has become a special science itself which is more
separated from mathematics, physics, or biology, than these branches
are separated among themselves. The width of the gap that has
separated science from philosophy became noticeable when the rise of
completely new theories like the theory of relativity produced a con-
fused situation among the scientists. The contribution of the philoso-^
phers trained in their special field toward a clarification of the new con-

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modern science and its philosophy

cepts and their integration into the whole system of our knowledge
has been all but negligible. The students of philosophy trained in the
traditional way have mostly studied the theory of relativity and quan-
tum theory from superficial popularizations which were written by
“physicists” who, in turn, had no training whatsoever in the logical
analysis and philosophy of science. Therefore, their popular writing is
imbued with their “chance philosophy” which they have picked up
somehow. Concepts like space, time, causality are used according to
these “chance philosophies.” In this way, again, their own traditional
and sometimes obsolete philosophy has been returned to the philoso-
phers in the disguise of the gospel of “science.”

To form an estimate of the width and the depth of the abyss which
we have mentioned again and again, we have only to make an attempt
to locate a philosopher who has a “clear and distinct idea” of, say, the
real issue in the old conflict between Copernicus and the Roman
Church, let alone of the conflict between the Newtonians and Einstein.
We would find very few. But it seems ob\'ious that nobody can grasp
the philosophic meaning of an issue in the history of human thought if
he does not understand the issue itself— and by “understand,” I mean
“thoroughly understand.”

Among philosophers the apology is current that it is just impossible
for them to have an exact insight into a scientific issue because the
sciences have become, in our time, so highly specialized that only the
specialist can have a thorough understanding. But if this is so, how
again can one have a philosophic judgment about an issue that one
understands only superficially because the matter is too complicated?
In this situation a great many philosophers have chosen to establish as
their redoubt a special field of philosophy outside the field of science.
To master this field one supposedly needs only an acquaintance with
the prescientific knowledge that is familiar to the man in the street.
According to this program of action, the philosopher investigates the
concepts and beliefs that are the logical basis from which the experi-
ence of our everyday life can be derived. On this level we make free
use of words like “time,” “space,” “existence of external objects,” in
the sense in which the man in the street uses these expressions. The

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science teaching and the humanities

special sciences like mathematics, physics, biology, as isolated branches
of knowledge, are taken for granted and the policy of nonintervention
is upheld. These recognized special sciences have been bom somehow.
They thrive happily without bothering about philosophic analysis.
The philosopher wants them to be happy in their innocence and not
to intmde into his “living space,” which is located between and above
and below the domain of these isolated special sciences.

Actually, these autonomous sciences exist only in the oversimplified
scheme set up by a large group of philosophers. The domain between
mathematics, physics, biology, history, is exactly of the same stuff and
has exactly the same logical structure as the domain within physics or
within mathematics. The borderlines between the special sciences are
drawn only for the sake of the division of labor and not for any pro-
found philosophical reasons. The special fields of physics and chemistry
were regarded for centuries as being of an essentially different nature,
since physics has to do only with quantitative changes while chemistry
inquires into qualitative or even substantial changes. Today we have
between physics and chemistry two new special fields— physical chem-
istry and chemical physics— which replace the mysterious something
that was supposed to be the philosophic link between physics and
chemistry.

The schools of thought that have advocated the separation of phi- '
losophy from science have certainly tended to cooperate in the integra-
tion of the sciences, but they perform this job by using as binding ma-
terial some prescientific stuff, while we leam from our last example
that the binding material between the special sciences is itself a full-
fledged science. But another school of thought, which claims to be very
up-to-date, takes an attitude that we may call an attitude of defeatism.

It leaves the special sciences untouched and autonomous. But according
to this school, philosophy does not even attempt to fill the gaps between
these special sciences but plans to build up a completely separated
stratum of knowledge “beyond science.” This "knowledge” is claimed to
be completely independent of any advance of science proper, for it is
based only on the prescientific experience of mankind.

We may distinguish two groups within this school. Both insist thaf

modern science and its philosophy

when the scientist has done his job as thoroughly as he can, the phi-
losopher’s job begins. When, for example, the physical laws of motion
are established by the scientist, the philosopher, says the first group,
steps in and puts his particular questions. The scientist has formulated
by his laws how motion takes place, what it is like, and so on. But the
philosopher wants to know what motion is, with the emphasis on the
“is.” While the scientist explores the observable attribute of motion,
the philosopher wants to find out the “being,” the “essence,” of motion.
This essence of motion can be discovered on the basis of our pre-
scientific knowledge about motion and cannot be affected by any
further advance in our science of mechanics. To this group belongs the
present-day neo-Thomist.

The second group starts also from the special sciences as having ac-
complished their job. But instead of looking for the “being” of things
this group claims that these special sciences take some “presupposi-
tions” for granted without investigation, such as the existence of ma-
terial bodies, the law of causality, the law of induction. Then, they say,
the philosopher has to step in and investigate whether these presupposi-
tions are correct. When I hear this claim, I have sometimes the feeling
that the shoe may be on the other foot. For quite frequently scientists
investigate the presuppositions that philosophers have taken for
granted without investigation. The founders of non-Euclidean ge-
ometry, Gauss, Lobatchevski, and Bolyai, doubted the axioms of
Euclidean geometry. Einstein doubted the axioms of Newtonian
mechanics, while a great many philosophers believed in these axioms
as eternal truths. Moreover, it is quite debatable whether “presupposi-
tions” like the existence of material bodies really play any role in
science and whether presuppositions that do play a substantial role
can be investigated by any method which is not scientific itself. What-
ever may be our final judgment about this investigation of presupposi-
tions, the practical effect of this philosophic school is again the es-
tablishment of philosophy as a special science besides mathematics,
physics, economics— and the perpetuation of a wide gap between
science and the humanities in our educational system.

The role of philosophy as an integration of human knowledge is

science teaching and the humanities

ignored, or, at least, neglected; consequently, the educational values
intrinsic in mathematics or physics are not exploited. These special
sciences are reduced to the status of useful knowledge without truth
value while, on the other hand, “philosophy” becomes a type of dis-
course without contact with the advance of science and, therefore,
without contact with the evolution of human intellect.

From these considerations, it seems obvious that the traditional
teaching of philosophy may have contributed considerably toward
sharpening the thinking of students and giving them a certain touch of
sophistication, but has certainly made little contribution toward the
synthesis of human knowledge which should be the chief goal of
liberal education.

5. Neo-Thomiam and Dialectical Motertolism

There is a suggestion which has been widely discussed during
recent years— the idea of Robert M. Hutchins, Chancellor of the Uni-
versity of Chicago. The essential point of his thesis is that we have to
base the integration of knowledge taught in our colleges on the last
available synthesis in the history of thought, on a kind of “standard
tradition.” According to this group, the spokesman of which has been
the philosopher Mortimer ] . Adler, the last system in history that has
really achieved a synthesis of science, ethics, politics, and religion is
the philosophy of St Thomas Aquinas. His Summa Theologiae
and his Summa CathoUcae Fidei contra Gentiles present a coherent
system in which, from the same set of principles, not only astronomy,
psychology, ethics, and politics are derived logically, but also the be-
havior of the angels— for example, whether the speed of their flight is
finite or infinite.

It seems, of course, debatable whether actually Thomism is the last
coherent system that has attempted or achieved such a sweeping
synthesis. Some people would, certainly, claim that the philosophy of
dialectical materialism, which is the ofBcial basis of education in the
Soviet Union, is ajlso a set of principles from which are derived not
only physical science but also the laws of history and sociology. Just as
well as Thomism this more recent system claims to give guidance not

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only in scientific research, but also in the question of what is a “good
life.”

The basic contention of Hutchins and his group is that a synthesis
which may not be perfect is preferable to no coherent synthesis at all.
There is no doubt that it is the chief asset of Thomism that such
disparate subjects as astronomy and theology can be regarded as con-
clusions from one and the same set of principles. But disregarding
theology, hardly anyone would claim that Thomism is a good system
from which to derive an answer to the question whether the New-
tonian or the Einsteinian mechanics is preferable.

In the same way, the chief asset of dialectical materialism is the fact
that the laws of physics are derived from the same principles as the
laws of human societies. We learn from the textbooks of dialectical
materialism that, for instance, the law of the transition of a capitalistic
society into a communistic one follows from the same principle as the
transition of water into steam. Both are conclusions drawn from the
dialectical principle that quantitative changes eventually become quali-
tative changes. But if we are not interested in the synthesis of physics
and sociology into one set of principles, hardly anyone would claim
that dialectical materialism is the best foundation of physical science—
j-for example, the most helpful interpretation of the evaporation of
liquids.

Dialectical materialism has, as a matter of fact, nowhere been
chosen as a basis of education except in countries where the govern-
ment has been committed to Marxist economic and political principles.
In this case, there is clear advantage in having these principles linked
up with the laws of physical science by a common set of principles.
With the same right we can assume that Thomism is not commendable
as a basis of education except where the government is committed to
the political and religious doctrine of the Catholic Church. For it will
enlist science by regarding science, politics and religion as derived from
common principles.

There is, on the other hand, no doubt that in an education which
emphasizes the integration of human knowledge, much more attention
than usual should be given to the systems that historically have per-

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formed such an integration, however we may judge the actual political
and religious way of life which is coherent with this system. The student
should get a good and unbiased presentation of both Thomism and
dialectical materialism as syntheses of human knowledge. But to make
either of these systems the main or exclusive basis of education in the
philosophy of science can be justified only if a particular political and
religious indoctrination is intended.

6. Integration of Science and Philoiophy

Before we can set up a constructive plan for bridging the gap be-
tween science and philosophy and, as a result, between science and the
humanities, we have to remove the chief obstacles blocking the way
toward this goal. As we have learned, the two principal obstacles are,
first, the exaggerated belief of scientists in specialization which some-
times leads even to a prejudice against general ideas and, second, the
recent tendency of the schools of philosophy to establish “philosophy”
as a new special science, instead of working on the synthesis of
knowledge.

The negative attitude of many scientists is based on their convic-
tion that any trespassing beyond the limits of one’s own field would
lead to unavoidable superficiality. Therefore, the genuine scientist has
to mind his own business and keep within the fences of his own de-
partment. There is, of course, a grain of truth in this argument of
avoiding superficiality. However, it does give only one side of the
picture, for the advance of science has revealed not only more and more
complexities in science, but also more and more cross-connections be-
tween the “isolated” special branches. By this fact it has become much
easier than formerly for one man to grasp the findings of several spe-
cial fields. We have only to consider die example of physics and
chemistry.

If we want to get a sound judgment of how, despite the abundance
of factual material, to acquire a thorough knowledge across depart-
mental lines, we have to ask, for example, how some people have man-
aged to become experts in a field like biophysics. They certainly did
not do it by a thorough study of the whole of physics plus the whole

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modern science and its philosophy

of biology, for this cannot be achieved in one lifetime. Instead, they
acquired a balanced survey knowledge in both fields, physics and
biology, and tried to acquire a really thorough knowledge in those
parts of physics and biology which are relevant for the interaction of
the phenomena of life with physical phenomena. As a matter of fact,
the behavior of the scientists who have worked within a traditional
field like physics has not been different. An average physicist will sur-
vey first general physics and then obtain a detailed acquaintance with
his special field within physics. If he wants to become a biophysicist
his survey information has to be broader, but his field of special in-
terest need not be larger than the special field of an ordinary physicist.
Moreover, to be quite truthful, the average physicist learns some part
of physics outside his special field only through popular generaliza-
tions. This is frequently true for the theory of relativity. The individual
physicist is, of course, not to blame for this situation, for without using
popularizations he would not be able to get any information about
important fields of his science.

From these remarks it becomes obvious what must be the train-
ing of the “philosopher of science” if his goal is a synthesis of human
knowledge. He has to acquire a survey knowledge of several sciences
and a thorough and precise knowledge of those parts of each special
field that are relevant for the relations across the borderlines and for
the relation between science and human behavior.

Some people may object that a survey knowledge would not be
sufficient, for one cannot know what part of science will be relevant
for the purpose of philosophy before the integration has been actually
achieved. There may be some truth in this argument, but it proves too
much, For according to this argument, every physicist must have a
thorough knowledge of the whole of physics; otherwise he cannot know
what knowledge may be relevant for his special field of physics. Noth-
ing can be done about it and he just has to take the risk in his training
as a physicist. He will learn by and by to smell what is relevant and
what is not. No greater effort is, in principle, required of the philos-
opher who wants to acquire a training in the philosophy of science.
There is no doubt, however, that evenfa. survey knowledge in the sci-

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science teaching and the humanities

ences^ill take so much of his time that he will not be able to get the
training that a philosopher has to get if he goes into “philosophy as a
special science.”

But it may be sufBcient for a student who specializes in the philos-
ophy of science and wants to take his Ph.D. in philosophy to get along
with a survey knowledge in the history of philosophy, without learn-
ing the details of all the opinions that have been uttered through two
or three thousand years. Every philosopher of science should, of course,
be familiar with the ideas of the great thinkers like Plato, Aristotle,
Thomas Aquinas, Leibnitz, Descartes, Kant, Nietzsche. But it is per-
haps sufficient if this special candidate becomes familiar with the
language of these men and knows how to locate their ideas within the
great stream of the evolution of scientific thought. This would leave him
time and, more important, the leisure to acquire a good survey of the
physical and biological sciences. He would concentrate his effort on
those parts of these sciences which are the most relevant for judging
the borderline problems arising between the special sciences and be-
tween science and traditional philosophy. He would concentrate, for
instance, in mathematics on problems like the “truth of non-Euclidean
geometry”; in mechanics on the role of “absolute motion”; and, in par-
ticular, on the ties between mathematics and physics, such as the dis-
tinction between mathematical and physical truth of geometric axioms.
He would, of course, try to acquire a thorough understanding of Ein-
stein’s theory of relativity, of Heisenberg’s principle of uncertainty, of
Bohr’s complementary concept of nature, and so on. In traditional
philosophy he would try to understand the approaches of different
schools to the question of what is the precise borderline between
physics and philosophy. He would try to learn the answers of the great
philosophers to questions like: What is the logical status of the general
laws of nature? Are they a result of experience or of reason or of what?
What are the roles of chance and of causality in the general laws of
nature and in their application to observed phenomena?

Teachers of philosophy with a similar type of training could give to
the students reliable information about the problems of the “philos-^
ophy of science” and of the “integration of sciences.”

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modern science and its philosophy

But tihen we are confronted by a further task. If we know even the
problems, do we know also the solutions? What should we present to
the student as the result of the integration of science? One should give
him reliable guidance without providing him with a “chance philos-
ophy” which may be either the result of an old and now obsolete tra-
dition or just the fashion of a year and a certain social group.

There is no doubt that the integration of knowledge on the college
level can be promoted among the students only by the use of philosophi-
cal and historical argument. However, the starting point has to be
living science itself. Philosophical and historical discourse must ema-
nate from this source. There are quite a few good reasons for this, but
it may be sufficient to consider the practical reason that in no other way
can philosophy and history be made palatable to the student of science,
and he will fail to appreciate this unusual food if he has no appetite
for philosophical and historical ideas. It would be, of course, a poor
teaching method just to add to the traditional presentation of science
some philosophic spice or sauce. We have rather to give to the presenta-
tion of science itself a philosophic touch.

The teacher of the special sciences will perhaps be afraid lest time
would be wasted by such a treatment. The student would pay for this
philosophical and historical touch by a deficiency of information in
science proper. But it seems to me that this new approach will rather
save time. For by this method a great many laws of physics, for ex-
ample, could be much more attractively presented to the students than
by traditional methods. However, I do not mean that the approach
should be made by one of the numerous metaphysical systems that
have been invented during the ages for the purpose of an integra-
tion of human knowledge. Every attempt of this kind would introduce
very questionable doctrines into the teaching of science and would
lead to disaster. We have to make use of the philosophic argument
that has grown up on the soil of science and has been fed with the
blood of science. We must never forget that metaphysics divides people
and science unites them.

If we try to build the bridge between science and philosophy, our
first step will be to present to the students their own special science as
a chapter in the book of human knowledge. Every scientist is con-

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science teaching and the humanities

fronted with the amazing fact that it is possible to derive from a few
simple principles by means of logical argument a wide range of facts
which can be checked by actual observations. The existence of these
principles allows us to put the phenomena of nature into our service,
for they enable us to construct methods by which the outcomes of physi-
cal processes can be predicted from the start.

Philosophy of science is concerned with the nature of this method
or device which man has invented in order to bring about the predic-
tion of physical phenomena. To have a certain understanding of this
device is a basic requirement for everyone who wants to understand
the history and the behavior of mankind in past centuries, and in our
own.

An understanding of the logical structure of science is a long step
toward the understanding of the meaning of statements in any domain
outside science proper and, indeed, toward judging truth of any kind.
In fields like ethics, politics or religion, we have also to distinguish
clearly between the factual content of a certain doctrine and the sym-
bolic language in which the statement of this doctrine is couched. The
example of physical science is a guide in a more difficult world and
will help us to disentangle statements of religious or political principles
with respect to whether they are really statements about observable
phenomena or only attempts to use a certain type of symbol.

In physics this analysis is comparatively simple and not so loaded
with emotional and egotistic elements. If someone asks people in the
strongest language to “follow the voice of their conscience” or to “fol-
low the will of God," this bid will be empty if he is not able to describe
the criteria by which we can know whether a “voice” is actually the
voice of our conscience or how actually to find out the will of Cod. The
student of science who has been trained in the "understanding” of
science will immediately turn his attention not so much to the strength
of the language, but to the question of who is authorized to interpret
the will of God.

7. Role of the Human Mind

By logical and empirical analysis the student will learn that the
principles of science are neither “proved by reason” nor “inferred by

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induction from sense observation.” They are a structure of symbols
accompanied by operational definitions. This structure is a product
of the creative ability of the human mind and consists of symbols
which are products of our imagination. But the truth of this struc-
ture can be checked by observations that can be described in every-
day language. By logico-empirical analysis the creativity of the hu-
man mind emerges as the primary factor in science. Thus the stu-
dent will learn that the role of this creativity in science is by no
means inferior to its role in the humanities and even in art or religion.
And we now can understand that the emphasis on science teaching will
no longer interfere with interest in the humanities but will rather sup-
port it.

I However, the role ascribed to the human mind by logico-empirical
analysis does not exhaust the contribution of science teaching to the
understanding of the human aspect in our picture of the world. For
by logico-empirical analysis the role of the human mind is only hinted
at in a rather abstract way. But our imagination and inventiveness are
much too limited to enumerate and discuss all possible principles that
the creative ability of the scientists may set up in order to derive the
wide range of phenomena of our experience. For this we have to study
the principles that have been actually set up in history. We have to
complement our logico-empirical analysis— where “empirical” implies
individual experiences— by “historical analysis,” which is empirical not
for the individual but for the human race. The history of science is the
workshop of the philosophy of science. We have to teach the student
all the relevant principles that have been set up in the course of history.
And we mean by history extension in time as well as in space, the de-
velopment of structures of science through the ages and over the sur-
face of our globe.

In this way the logico-empirical analysis gains life and color and
becomes a living link between science and the evolution of the human
race. The average textbook of physics tells us very little about the evo-
lution of the principles of this science, except some dates of anniver-
saries. Very often these books speak about ancient and medieval sci-
ence in a derogatory way; they claim not to understand why for ages

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people were not able to discover such a simple law as the law of in-
ertia, which today every schoolboy knows is an obvious result of our
everyday experience or is even self-evident. But despite these smug
remarks the same textbooks are not able to formulate this law of inertia
in a satisfactory way. They even block the understanding of this and
similar principles. For it is clear that a principle which intelligent men
have not found through centuries cannot be as obvious as the state-
ment presented by these books as the law of inertia. This complacent
attitude imperils even the understanding of the evolution of thought
and helps to spread the spirit of intolerance and bigotry among the
students, while an attitude of adequate logico-historic analysis would
contribute toward good will between people of different backgrounds
and different creeds.

The best way to help the student to understand the steps in the
evolution of human thought is to present to him in elaborate detail the
chief turning points in the evolution of science, with the emphasis not
so much on the discovery of new facts as on the evolution of new prin-
ciples of change in the symbolic structure. It would be, for example,
of the greatest importance to discuss thoroughly the conflict between
Copernicus and the Homan Church (or, for that matter, the Lutheran
Church), I think that every student of science and the humanities
should have a clear understanding of this issue, which was one of the
greatest and most interesting in history. If this subject were discussed
thoroughly and competently, the student could get a good understand-
ing of the eternal conflict between established patterns of presenting
the facts and attempts radically to alter the symbolic structure of
science. He would learn that the tendency to preserve the old pattern
of presentation is often disguised under the name of “common sense,”
and how the appeal to common sense has been used in the history of
mankind to cloak the interest of established governments and churches.
For, as he would learn in particular, the role that the interaction among
science, philosophy and religion has played in the justification of po-
litical aims is very great.

Equally, students of science and philosophy should learn exactly
what were the issues between Descartes and Newton and between-

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modern science and its philosophy

Newton and Leibnitz. From these disputes has arisen what we now
call the classical physics of the nineteenth century, which until today
has been the basis of the training in science that our students get in
colleges of engineering or liberal arts. To grasp these issues would help
them to understand our present science as a dynamic living being. This
would not happen if they were confronted only with the desiccated
and artificially stuffed skin of science that is presented in most of the
current textbooks.

8. Science and Political Ideologies

If the students get an understanding of the earlier turning points in
science, it will be much easier for them to grasp exactly the meaning
of the turning point around 1900, when our twentieth-century science
was bom.

This last turn has been dramatized by the phrases “crisis of classical
physics” or “decline of mechanistic physics” or “refutation of material-
ism.” If one has been trained to analyze the nature of a “turning point
in the history of science,” one will be less inclined to believe that the
“crisis of classical physics” is a “crisis of rational thinking” or even a
justification of an irrational approach to science.

As we have already mentioned, it is not suflBcient to approach these
turning points of human thought by logico-empirical analysis only, for
the human mind is not strong enough to carry out an exact analysis of
such a complex stmcture. One has to study classical physics as an ex-
.tinct organism, which grew up against immense obstacles, defeated its
opponents, and then turned out to be no longer fit for survival. With
this training one would have a clear understanding of, say, the broad
analogy between the fight of medieval philosophy against Copernicus
and the fight of modern Newtonian philosophy against Einstein.

Students who have this kind of logical and historical training will
easily see through attempts to exploit the “breakdown of Newtonian
physics” and the “defeat of materialism” in order to justify a return
to ancient “organismic science.” They will be, moreover, on their
guard against attempts to exploit this “crisis of thought” in a fight
against liberalism and democracy, or, for that matter, against all pro-

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gressive trends which have been historically labelled "materialistic’’ or
“atomistic’’ or “mechanistic."

By this approach the student of science would be led in a natural
way to an understanding of the struggle among rival ideologies. It will
be a great attraction for him to approach these problems starting from
the role that has been played by his own special field. The student of
science will get the habit of looking at social and religious problems
from the interior of his own field and entering the domain of the hu-
manities by a wide-open door and not by the rear door of some isolated
humanity course which he may take for "distribution” He wiU need
neither a spoon feeding of trivial information nor a stuffing with techni-
cal material that is of no real profit for his general education.

There is no better way to understand the philosophic basis of politi-
cal and religious creeds than by their connection with science. The
student who understands the relation of his science to these creeds
has an access from an inside track. He will easily and confidently cross
the bridge between science and the humanities.

The attentive student of science will notice soon that the tradi-
tional symbols of science have a life of their own. They persist in a
changing world where the scope of science is continually growing.
This point is made particularly clear by focusing the attention of the
students on the turning points in the evolution of scientific thought.

The student will learn, for example, in what sense materialism has
been encouraged by the physics of the nineteenth century and how
this in turn was anticipated to a certain degree by the Epicurean School
in old Greece. He will learn how the transition from medieval physics
—which was based, in its turn, on the Aristotelian school of Greece—
to the physics of Galileo and Newton found its continuation in the
school of Laplace at the end of the eighteenth century at the time of
the great French Revolution. He will appreciate, then, how the fight of
Newtonian (mechanistic) physics against Aristotelian (organismic)
physics became connected with the fight of liberalism and tolerance
against feudalism and bigotry.

He would thus understand that what scientific and corresponding
political (ideologic) issues have in common is the use of the same sym*

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modern science and its philosophy

bols, with their wide range of connotations. In this way the student of
science would learn to appreciate the great value of symbols in the
history of human thought and, for that matter, in the history of human
behavior.

Whoever has understood these historic issues correctly will attain a
sound judgment regarding the last great transition, around 1900, when
mechanistic physics had to give way to a more general approach. The
transition from the nineteenth-century to the twentieth-century physics
culminated in the relativity and quantum theories which, in turn, have
led to new philosophic slogans describing this transition as an “over-
throw of the concept of absolute time and space” and an “overthrow
of physical determinism.” The student who has been through the train-
ing in logico-empirical and historical analysis will assess the attempts
that have been made to exploit the new physical theories for the benefit
of particular religious and political ideologies. He will see through
the argument by which the “overthrow of eighteenth- and nineteenth-
century deterministic physics” has been used in the fight against liber-
ahsm and tolerance, since these creeds had grown up in a period of
mechanistic and deterministic science. He will understand that the
breakdown of mechanistic physics did not actually imply a return to
organismic physics, which was, historically, connected with the political
and religious doctrines of the Middle Ages. He will understand why
twentieth-century Fascism has gladly interpreted the “crisis of physics”
as a return to organismic physics which could provide a “scientific”
support for a return to some political ideas of feudalism.

But, above all, the well-trained student will understand the para-
mount fact that, actually, mechanistic physics was replaced^ not by
any organismic physics, but by an entirely new approach to science by
logico-empirical analysis, which has been in the twentieth century the
starting point of all the new physical theories.

If science is taught in this way, the emphasis on science and tech-
nology toiU no longer be an obstacle to a liberal education of the stu-
dent. The deplorable gap between science and the humanities will not
arise, let alone widen. On the other hand, the intensive study of science
as a living being will give to the student of it a profound understand-

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ing of the role of the human mind in human action, which is the very
goal of instruction in the humanities.

9. Science and the Historical Systems of Philosophy

By emphasizing the historical evolution of scientific thought the
student will learn, moreover, that the human mind has not always been
satisfied with the logico-empirical analysis of science, since this presen-
tation of science is only satisfactory for the “purely scientific” purpose
of predicting and mastering the observable phenomena of nature. But
the phenomena are derived from principles that are couched in sym-
bols and, as we have already hinted, these symbols have their own
life, which is to a certain degree independent of the evolution of sci-
ence proper. These symbols which are created hy the scientists may
even become occasionally a Frankenstein’s monster. However, as these
symbols are not unambiguously determined by the scientifically ob-
served facts, they are strongly influenced by extrascientific factors. The
choice of symbols is, as a matter of fact, very dependent on the impact
of current social and religious movements. These influences are largely
responsible for the decision whether one prefers rigid pieces of mat-
ter as fundamental symbols (materialism) or whether one builds up all
concepts from mental elements (idealism), whether one picks as the
ultimate building stone a nondescript reality (realism), or whether
one starts from elements that cooperate toward a certain goal (organ-
icism). Every satisfactory instruction in the philosophy of science has
to discuss these choices of symbols on the basis of logical and historical
analysis. The influence of political and religious trends on the choice of
these symbols should by no means be minimized, as is often done in the
presentation of the philosophy of science. On the other hand, if “meta-
physical integrations of science” are discussed, particular attention
should be given to those integrations that have played a role as bases of
ideologies. For this reason, doctrines like Thomism or dialectical mate-
rialism should be carefully and correctly presented to the student and
more time should be devoted to them than is devoted to some sophisti-
cated systems that have played only a small role in human life and
human actions. ‘

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modern science and its philosophy

If the foregoing plan is followed, we shall have no more graduates
in science who have no clear idea of the teaching of men like Aristotle,
St. Thomas, and William of Occam or, for that matter, of Hegel, Marx,
and Lenin. The type of science graduate who is without humanistic
training will disappear just like those who have not even a clear picture
of what the contribution of Copernicus was to our world.

The educational value of this type of instruction for science students
seems to me beyond doubt. However, there is still the question of where
to find a place for it in the curriculum. The most natural plan probably
would be to teach the science courses of broader scope according to this
method. This would hold, for example, for the elementary courses in
coUege physics, chemistry and biology. Such a start would certainly be
very stimulating and helpful for the beginning students. However,
since these students have not the background necessary for the study
of subtle problems, these "survey courses for beginning students”
should be complemented by “survey courses for advanced students.”
These would be appropriately given just before graduation. They
should answer the questions that were prompted by the elementary
courses and treat them on a higher level. These new courses should not
be “superficial surveys” as this tenn is often understood, but should
give a bird’s-eye view of the results of science, with emphasis on spe-
cial unsolved problems. These courses could be given according to the
suggestions of this paper.

If there are not a suflScient number of science teachers in a college
who are interested and trained in this plan of instruction, one or two
“special” courses outside the usual science curriculum should be estab-
lished, to be given by the few available teachers who have the necessary
training and inspiration for this task. One may give these courses un-
der the tide of “philosophy of science” or “foundations of science” or
“science and the humanities.”

The present trend toward general education has, in some colleges,
led to the establishment of science courses for nonscience students.
The program of these courses emphasizes the bridge between science
and philosophy or science and the humanities somewhat along the lines
tliscussed in this paper. In these plans, however, only the nonscience

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student will be presented with the educational value of science, while
the concentrator in science will not be able to give information about
the role of science in human society to his future pupils or to his
community in general. The questions regarding science that are most
interesting to the general public should be answered by a compe-
tent and responsible man; and this obviously can be only the science
teacher in the high school or college.

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the place of logic and metaphysics in the advancement
of modern science

O NE of the most brilliant writers on intellectual history, Carl
Becker, claims that the most important event in this field in
modem times was the shift in the place of logic in science.
According to Becker, the high esteem in which logic had been held by
the scientist in the time of St. Thomas Aquinas and through all the
Middle Ages declined in the period of Galileo and Newton. But at that
time this decline was not yet fully understood. “The marriage of fact
and reason,” as Becker puts it, “proved to be somewhat irksome in the
nineteenth century and was altogether dissolved in the twentieth cen-
tury.” The modem, twentieth-century, physicist lives in an "atmosphere
which is so saturated with the actual that we can easily do with a
minimum of theoretical. . . . We have long since learned not to bother
much with reason and logic.” To describe the spirit of twentieth-
century physics, which emphasizes facts and minimizes reason, Becker
says;

Experiments seem to show that an electron may, for reasons best known
to itself, be moving in two orbits at the same time. To this point Galileo’s
common-sense method of noting the behavior of things, of sticking close to
the observable facts, has brought us. It has at least presented us with a fact
'that common sense repudiates.

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logic and metaphysics in modern science

I do not think that Galileo was actually less concerned with logical
consistency than Aristotle, nor do I think that Einstein’s theory of gravi-
tation is more factual and less rational than Newton’s. I shall not enter
here into historical arguments; I shall restrict myself to investigating
the nature and the bearing of that “most important event in the intel-
lectual history of modem times” which Becker stresses so strongly.

The pre-Galilean period, say until about 1600 a.d., adhered to a kind
of organismic world view founded largely upon the philosophy of Aris-
totle and the medieval schoolmen. The "mechanistic” conception of
nature began with Galileo and Newton. Its peak, however, was reached
in the first half of the nineteenth century. According to Becker, this
whole period including the Middle Ages, the Renaissance, and the
eighteenth-century enlightenment, was characterized by the belief that
there is a rational picture of the world, there is a way by which man
can comprehend nature by reason. But in the twentieth century this
belief faded more and more. An acute observer would have already
noticed this fading in the Galilean period when the confidence in the
scholastic type of philosophy declined. More and more, the "cli m ate
of opinion,” as Becker calls it, became less logical and rational and
more factual and in some ways irrational.

We shall probably not seriously believe that science has ceased to
be logical. If we use this word in its technical sense, everyone will
agree that a science that repudiates logic has never existed and can
never exist. Now, what did Becker really mean by his “decline of
reason and logic” in the twentieth century and even in the approaches
to this century? Why did he believe that the organismic medieval
world picture was rational as well as the Newtonian and Laplacian
mechanistic picture, while the twentieth-century picture of physics,
characterized by relativity and quantum theory, is no longer concerned
with reason?

We shall understand this point better if we direct our attention to
the fact that, according to Becker, this decline of the rational world
view had already started in the Galilean period and is, therefore, some-
how connected with the d^line of scholastic philosophy. 'The common
feature of medieval and of mechanistic physics seems to me to be that

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modern science and its philosophy

their principles seemed to have a certain plausibility by themselves.
Medieval science derived all observable phenomena from the principle
that they are somehow analogous to the well-known phenomena in a
living organism. Seventeenth- and eighteenth-century science, in turn,
preferred the analogy to simple mechanisms which are familiar to us
from our everyday life experiences. Not only were the principles con-
firmed by demonstrating that the conclusions drawn from them were in
agreement with observed facts, but also the principles themselves used
to be directly confirmed by a kind of short cut. If a law of physics was
in agreement with the organismic or mechanistic analogy, this agree-
ment accounted for a certain degree of confirmation. A more careful
analysis would probably lead to the result that the organismic as weU
as the mechanistic principles of science drew their plausibility from the
fact that they seemed to reflect faithful pictures of our everyday ex-
perience. In scientific theories a long chain of intellectual and experi-
mental work connects the principles of a theory with the protocols of
observation. The organismic or mechanistic principles, however, could,
it was believed, be confirmed directly by a very obvious type of ex-
perience. Everybody knew that a piece of earth tliat is dropped falls to
the ground. It therefore seemed obvious that the earth as a whole could
not remain suspended in space and circulate around the sun. It was to
fall to the center of the universe like a small piece of earth. This tend-
ency toward the center as the natural place of the heavy element earth
seems to be a principle of physics with firm roots in everyday experi-
ence. In the same way, a mechanistic principle like the law of inertia
seemed to be directly confirmed by the most familiar facts of our daily
experience.

In this sense we can say that the organismic as well as the mechanis-
tic physics were based on principles that could be interpreted directly
in terms of everyday experience. The validity of the principles did not
need any further confirmation by the development of more refined
methods of observation and theoretical argument. Science, in those
days, was based on principles to which an eternal validity was as-
cribed. They appeared to be “rational” or “reasonable” or, expressed
in a loose way, “logical.” The philosophers of the eighteenth-century

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logic and metaphysics in modern science

enlightenment still felt that theirs was a world view, provided com- \
pletely hy reason. The age of enlightenment shared this belief in
reason with the “dark” Middle Ages. This is the historical point that
Carl Becker wanted to make in his book. In the nineteenth century,
according to Becker, a drive was initiated to tell reason that it had to
know its place, which was considerably lower than previously; but in '
the twentieth century, science emancipated itself from reason alto-
gether.

After these few remarks about the place of reason in the science of
past centuries, it is obvious what the characteristic of twentieth-
century science is. With the rise of non-Euclidean geometry, the
physics of relativity and the mechanics based upon the de Broglie
waves, the basic principles of physical science were no longer a direct
formulation of our everyday experience; they were no longer obvious
and plausible to common sense. Their only justification consisted now
in their property of yielding observable facts by means of a chain of
logical conclusions. The illusion disappeared that the principles of
science were of eternal validity or could at least be interpreted as con-
clusions from such principles. Therefore, one ought not to say that
twentieth-century science has no use for logic but rather that it has no
use for metaphysics. To interpret the principles of science as results of
our common sense leads to the opinion that they are self-evident and
cannot be refuted by further empirical checking. This belief is the very
core of the metaphysical interpretation of science.

One should rather reformulate Becker’s argument as follows: In the
period of Galileo and Newton the firm belief in the metaphysical
foundation of science faded a little. Mechanistic physics was less im-
bued with metaphysical argument than was medieval, organismic,
science. But the belief in Newton’s laws as results of the simple ex-
perience of everyday life had been bolstered up during the eighteenth
and a great part of the nineteenth centuries, although it was by no
means a common opinion among Newton’s contemporaries. With the
new physical theories of the twentieth century— non-Euclidean geome-
try, relativity and the quantum theory— the belief practically disap-
peared that the basic principles of physics ought to be plausible ac-

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modern science and its philosophy

cording to the criteria of common sense. The metaphysical conception
of science lost ground and the logico-empirical interpretation of the
scientific method became the method that was actually used. We can
see in the evolution of science from the seventeenth century to the
twentieth century the gradual decline of metaphysics in favor of a
positive conception, if we want to use the terminology of August
Comte.

I am using the term metaphysics here with a positive and precise
meaning; direct interpretation of the basic principles of science in
terms of common sense or everyday experience. I think that it is not
sufficient to characterize metaphysical statements as “meaningless.”
There are a lot of meaningless statements that are not at all “meta-
physical.” By using the term in the way I suggested we can probably
cover all the statements which have been made with the claim to be
metaphysical. Metaphysics, according to our way ot speaking, is cer-
tainly meaningless from the scientific viewpoint because the terms
“true” or “false” cannot be applied to these statements. Charles Morris
speaks, however, of a “metaphysical discourse.” I agree with him in
the sense that I regard metaphysics as a direct interpretation of
scientific principles in terms of the language of everyday life experi-
ence. “Interpretation” means translation. Metaphysics attempts a trans-
lation of the basic principles of science, but not according to a strictly
fixed dictionary; the univocal relation between a term and its transla-
tion has been replaced by an analogical relation. But we cannot tell by
any exact criterion what is a “correct” analogy. We shall elaborate this
conception of metaphysics more exactly toward the end of this paper.

If one even agreed that the place of logic and reason in science had
not lost in importance in our time, a great many people, including even
scientists and philosophers, would claim that the actual advance of
science had been promoted not by logic and reason, but rather by
intuition and metaphysics. Logic, so this argument goes, is useful only
for systematizing scientific knowledge and statements that are already
known; it can never be of any help in finding new statements and, still
less, fundamentally new theories. This assertion has been repeated
Again and again, but it cannot stand a critical test. If we include in

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logic arid mefaphysics in modern science

logic not only syntax of language but also the theory of meaning,
semantics, one could easily make a good case for the assertion that
the “experimental” theory of meaning, which has been advocated by
pragmatists and logical empiricists, is the very basis of twentieth-
century physics. Not only does it provide the method of presenting this
physics systematically, but one can also point out that the authors of
this new physics made explicit use of this theory of meaning. This
theory was one of the historical roots of the new physical theories.

It is hardly necessary to stress the fact that this theory of meaning
guided Einstein in his “restricted” theory of relativity as well as in his
general theory. When Einstein in 1905 introduced his interpretation of
the Lorentz transformation which was the essence of the special theory
of relativity, he pointed out that the statement “two events at a spatial
distance take place at one and the same time” cannot be used to derive
any observable fact. Therefore, this statement cannot be a part of any
physical theory. Einstein clearly understood that this statement needs
in addition a semantic rule or operational definition. In the develop-
ment of the general theory we again have statements of the type “the
rotation of this body is responsible for a centrifugal force.” Tliis state-
ment is regarded as a legitimate statement in Newton’s mechanics.
But Mach pointed out that such a statement cannot be used to derive
observable facts because it does not contain any rule by which one can
check by observations whether a body is rotating. This remark was one
root of the general theory and the theory of gravitation. This correla-
tion between the theory of meaning and Einstein’s relativity was fully
appreciated by Bridgman.^

It is perhaps less generally known that the development of quantum
mechanics also has its historical root in the empirical theory of mean-
ing. The decisive turning point in the history of quantum mechanics
was Heisenberg’s paper* of 1925. Until this date the state of the
quantum theory was characterized by Bohr’s theory of the hydrogen
atom, by the Keplerean orbits of the electrons around the nucleus
which obeyed the Newtonian laws with certain restrictions. Bohr’s

^ P. W. Bridgman, The Logic of Modem Physics (New York: Macmillan, 19271.

* W. Heisenberg, Zeitschrift fur Fhysik 33, 879 (1925).

^ 291

modern science and its philosophy

theory superimposed upon Newton’s laws the quantum laws, accord-
ing to which only some specific orbits could be performed without
giving rise to a radiation which according to classical physics would
destroy the orbit. This pre-1925 state of quantum theory can be
described as a “Newtonian mechanics patched up by quantum laws.”
Heisenberg, in the paper mentioned, was the first to replace Newtonian
mechanics, in his application to the movement of electrons, by a com-
pletely new physical theory which became known under the name
“quantum mechanics.” His starting point was exactly the experimental
theory of meaning. He says:

In this paper I am going to attempt to find foundations for a mechanics
of quantum theory. This mechanics is based exclusively on relations between
quantities that are observable in principle. . . . As it is well known, a very
relevant objection can be raised against the formal rules that are used in
quantum theory for the computation of observable quantities (e.g., the
energy of the hydrogen atom). These rules of computation contain as an
essential part relations between quantities that are unobservable in principle
(e.g., the position and the period of an electron). Therefore, those rules are
without any intuitive foundation if one does not expect that those quantities
which are at present unobservable will eventually be accessible to experi-
mental observations. . . . Under these circumstances it seems advisable to
make the attempt to bufld up a quantum mechanics that is analogous to the
classical mechanics but in which only relations between observable quantities
occur.

Accordingly, Heisenberg introduced not the position of the electron
but the Fourier coefiBcients of the radiation that is emitted by the atom
as a result of the Keplerean motions of the electron. These Fourier
coefiBcients developed later into Heisenberg’s matrices and Schrodin-
ger’s wave function.

Hence, the heuristic value of the “experimental theory of meaning”
is proved by the actual history of twentieth-century physics. It turned
out later that the actual formulation of the principles of the new
physics could not be achieved in this direct and simple way. It has not
been sufiBcient to use only observable quantities as terms in these prin-
ciples. One had to proceed in a more indirect and complex way. This
Uks been the case in relativity as well as in quantum mechanics.

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logic and metaphysics in modern science

If vre consider, as an example, Einstein’s theory of gravitation, the
principal part of this theory is the diflFerential equations of the gravita-
tional field. They contain mathematical symbols: the four general
coordinates in the space-time continuum, the ten potentials of the
general gravitational field, etc. One cannot lay down practical semantic
rules for these symbols as they stand in the general field equations. But
by mathematical conclusions we can derive results from these field
equations which can be translated by means of feasible semantic rules
into descriptions of actually observable facts. If, for example, we derive
the bending of light rays in the gravitational field of the sun, we obtain
statements in which the general coordinates in the space-time con-
tinuum can be connected in a clear-cut way with the spatial and tem-
poral distances which are measured by our traditional ways of measur-
ing length and time intervals. But such a connection cannot be laid
down in full generality. If, for example, we consider the statement “one
and the same factual event can be described by different sets of values
of the general coordinates in the four-dimensional continuum,” we can
hardly lay down practical semantic rules by which the operational
meaning of this statement can be defined in a simple way.

P. W. Bridgman maintained, therefore, that Einstein’s general
theory of relativity does not fulfill the requirements put forward by the
experimental or operational theory of meaning. According to these re-
quirements, one must give explicit operational definitions of all terms
that occur in the general principles of a theory. While, according to
Bridgman, the restricted theory of relativity was a brilliant example
of the use of operational definitions, he thinks that the general theory
has violated the requirement for such definitions.® There is no doubt
that on the way from the restricted theory of relativity to the general
theory the structure of a physical theory, as envisaged by Einstein, has
changed in a noticeable degree.*

The restricted theory of relativity nearly fulfilled what has been

®P. W. Bridgman, op. cU.; The Nature of Physical Theory (Princeton Univer-
sity Press, 1936).

* Albert Einstein: Philosopher-Scientist (vol. 7 of The Library of Lining Phi-
losophers, P. A. Schilpp, ed.; Evanston and Chicago: Northwestern Universit}^
1949).

modern science and its philosophy

called Mach’s “positivistic” requirement, according to which all prin-
ciples of physics should be formulated by using only observable
quantities as terms. The general theory made use of this requirement
only as a heuristic principle, as a hint of how to build up the system
of fundamental principles. These principles themselves, however, ful-
filled the “positivistic” requirement only in an indirect way. Einstein
replaced it, consciously and deliberately, by a weaker requirement: it
was merely required that from these principles mathematical con-
clusions could be drawn that were connected by semantic rules with
statements about observable facts.

Albert Einstein, in his Herbert Spencer Lecture given at Oxford in
1933, speaks about this change in the way in which the abstract prin-
ciples of physics are connected with the observable facts. This boils
down to a change of the place where the semantic rules or operational
definitions are attached to the abstract principles. Einstein speaks of
“the ever-widening logical gap between the basic concepts and laws on
the one side and the consequences to be correlated with our experiences
on the other.” He insists merely on the requirement that some results or
propositions in the system be connected with observational statements
by means of semantic rules. In his “Remarks on Bertrand Russell’s
Theory of Knowledge,” ® Einstein says:

In order that thinking might not degenerate into “metaphysics” or into
empty talk, it is only necessary that enough propositions of the conceptual
system be firmly enough connected with sensory experiences.

According to this new conception, the sentences that have to be
connected with sense observations by semantic rules are no longer the
general abstract principles (such as the law of conservation of energy)
but some special conclusions drawn from these principles. The “posi-
tivistic requirement” now means that there must be some consequences
of the general principles which can be translated into statements about
sense observations. The general principles themselves are the product

“ The Philosophy of Bertrand Bussell (vol. 5 of The Library of Living Philoso-
phers, P. A. Schilpp, ed.; Evanston and Chicago: Northwestern University, 1944),
p. 289.

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logic and metaphysics In modern science

of mathematical and logical imagination which has to be checked by
applying the “positivistic” or “operational” requirement.

The nature of a scientific theory in this sense can be understood
even more precisely if we consider the new “unified field theories” pro-
posed by Einstein and Schrodinger. A “unified field of force” is to be
constructed which contains the gravitational, the electromagnetic and
the nuclear field as special cases. Schrodinger, for example, introduces
sixty-four symbols which are the components of this unified field. He
does not lay down any semantic rules for these sixty-four quantities.
But if this theory is to be of any scientific value, he has to assume, as a
matter of course, that some special relations can be mathematically de-
rived from the principles which can be connected with observable
facts. He hoped, for example, that it could be derived that a rotating
mass which obviously produces a rotating gravitational field would
entail a magnetic field. One would be able to account in this way for
terrestrial magnetism.

From a psychological viewpoint Einstein describes this way of
producing theories by free imagination in a letter to the French
mathematician Hadamard.® According to this new conception, it is
true that physical theories are the product of free imagination, if we
take the word “free” with a grain of salt. But it must not be concluded
that these theories are products of metaphysics. For these theories are
subjected to the operational or experimental criterion of meaning,
though in a more indirect and complex way. The criterion of truth
remains ultimately with the checking by sense observations, as the
older “positivists” claimed. But we know now that this checking is a
more complex process than it was believed by men like Comte and
Mach to be.

If we applied the name "metaphysics” to a system of statements the
“truth” of which is judged according to the experimental criterion of ^
meaning, there would be no distinction between science and meta-
physics. We have, therefore, to reserve the word “metaphysics” as a
characteristic of systems the truth of which is decided on other grounds.

* J. Hadamard, An Essay on the Psychology of Invention in the Mathematical
Field (Princeton University Press, 1045). •

* 295

modern science and its philosophy

In metaphysics a statement or a system of statements is regarded as
“true” if our common sense imderstands the validity of the principles
immediately without having to draw long chains of conclusions from
these principles and without checking some of these conclusions against
our observations.

Such a metaphysical interpretation of twentieth-century physics
was given, for instance, by Eddington.’ He claimed that the validity of
our physical theories can be demonstrated by what he called “epistemo-
logical arguments.” This meant in his language that the principles of
physics have to meet some requirements emerging from common sense.
And these requirements are sufficient to determine our physics to such
a degree that even the number of the electrons in the whole universe
can be derived mathematically. Eddington’s argument is actually
“metaphysical.” We could call it “epistemological” only if we regarded
epistemology as a part of metaphysics. The point is that Eddington
derives his system of physics from everyday experience and not from
scientific experiments which are needed to check the results of a long
chain of conclusions from the principles. The requirements of “com-
mon sense” actually are that these principles should be a convenient
description of our everyday experience.

Certainly, men like Einstein and Schrodinger advanced their
principles by following some requirements of simplicity or beauty
which may also be regarded as requirements of common sense. But
they would never claim that the validity of the principles could be
proved without checking the conclusions drawn from these principles
by physical experiments.

If we want to compare the respective places of logic and meta-
physics in the actual advancement of science, we can point out two
ways in which logic has been instrumental in the advance of twentieth-
. century science. We have already described the heuristic value of the
experimental theory of meaning which played a decisive role in the
rise of relativity as well as of quantum theory. But logic has also played
in another way a guiding role in the advance of twentieth-century

’ A. S. Eddington, The Philosophy of Physical Science (New York: Macmillan,
1639 ).

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logic and metaphysics in modern science

science. And this way is connected with formal logic, or what we may
call ‘logical imagination.” Einstein, in particular, has described re-
peatedly how the building of formal systems of symbols, the successive
demolition, rebuilding and alteration of these symbolic structures, bas
had a great bearing upon the advance of new physical theories. In
his letter to Hadamard, Einstein gives a psychological description of
his creative work. He insists that the essential part in creative thinking ✓
is the free play with symbols. In his Herbert Spencer Lecture (1933),
Einstein says:

Experience, of course, remains the sole criterion for the serviceability
of mathematical construction for physics, but the truly creative principle
resides in mathematics.

This means, obviously, that the creative process in theoretical
physics consists, in some important ways, in the creation of symbolic
or formal systems by a kind of “logical imagination.” Among the sys-
tems created in this way, experience is responsible for the natural
selection that determines which system is the fittest for survival and
which has to be dropped.

In order to appreciate the place of logic, we have to consider the
shift in the conception of a physical theory that has developed from the
times of Mach to the times of Einstein. The operational definitions or
semantic rules are now no longer applied to the general principles
themselves but to some conclusions drawn from them. However, this
distinction should not be overstressed. It would be erroneous to be-
lieve that men like Ernst Mach actually believed that all principles of
physics were direct descriptions of experimental facts. In his paper on
the role of comparison in physics, Mach distinguished very precisely
between “direct description” and “indirect description.” The latter, he
said, is also called “physical theory.” He gives as an example the wave
theory of light. In this theory there is certainly no explicit operational
definition of the “light vector.”

As for the heuristic value of metaphysics, we may quote one of the
most prominent contemporary advocates of metaphysics, Jacques
Maritain. He says bluntly:

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modern science and its philosophy

It is true that metaphysics brings no harvest in the field of experimental
science ... Its heuristic value, as the phrase goes, is nil . . .

It cannot be of any help in promoting scientific research. He continues:

This universe in which metaphysics issues ... is not intelligible by
dianoetic or experimental means, it is not connatural to our powers of knowl-
edge, it is only intelligible to us by analogy.

This means in the usual language of the scientist: In metaphysics we
do not use either logical (dianoetic) or experimental argument, but
we interpret the principles of science in a metaphoric language. Meta-
physics attempts to interpret the general principles of science in a way
that is plausible to our common sense. The principles then become
analogous to the laws of everyday experience; they duplicate them, but
on a higher level. The law of conservation of energy becomes meta-
physically plausible because it is bolstered up by the well-known ex-
perience that objects of the physical world (stones, animals, etc.)
cannot disappear. We transfer the conception of “disappearing” to an
“object” called “energy” which is certainly not a physical object in
the sense that a table is such an object. Therefore “disappearance of
energy” can only be understood by “analogy” with the disappearance
of a stone. According to Thomistic metaphysics, in an expression like
"the being of God” or “the being of a spirit” the word ‘Treing” does not
mean the same thing as it does in “the being of a stone.” The meaning
of “being” on these “higher levels” is only understandable by analogy,
not by any direct operational definition or semantic rule.

I would not even go as far as Maritain in denying any heuristic
value in metaphysics. The description by analogies can occasionally
be of some psychologic value in setting up new principles. This was
even recognized by so staunch an opponent of metaphysics as Ernst
Mach in his paper on the role of comparison in physics.

But if we analyze a little further the nature of the actual metaphysi-
cal interpretations of physics, we soon notice one characteristic of them
that can easily become prohibitive to any future advance of physics.

I shall not now go into an elaborate discussion of this nature of
ifletaphysics. I shall restrict myself to showing by some examples that

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logic and metaphysics in modern science

philosopheis who went in for both metaphysics and science frequently
pointed out this characteristic of metaphysics. They stressed the point
that metaphysics is an attempt to interpret the general principles of
physics in terms of the language of our everyday life. In this way it is
possible to muster the support of our everyday experience to make
those principles plausible.

A very characteristic example is the French philosopher E. le Roy.
His goal was to prove on the basis of contemporary science that room is
left for metaphysics and even for a metaphysical conception of religion.
He especially liked to make use of the ideas that the famous French
scientist, Henri Poincar4, had advanced about the logical status of
science. Just at the turn of the century (1899) Le Roy published in
the Revue de M^aphysique et de Morale a paper in which he says:

Science departs from common sense and does not join it in its develop-
ment as science proper. Thus science by itself does not close the cycle of
knowledge and does not realize the unity of knowledge. Science needs there-
fore a prolongation and this will be philosophy ... in one way science
itself is a prolongation of common sense.

Common sense, science, philosophy, common sense form a cycle.

The term “philosophy” refers here, of course, to the same thing as
“metaphysics.” In these words we see clearly the place assigned to
metaphysics. Science departs from common sense by using a different
conceptual scheme; words are used in a different way. Science even
introduces expressions that have no meaning in the language of com-
mon sense. This becomes particularly clear if we consider the language
of twentieth-century physics. The theory of relativity uses expressions
like "one and the same object has different lengths relative to different
systems of reference,” and quantum mechanics uses expressions like
“if the position of a particle is a definite one, its velocity is always
indeterminate.”

According to Le Roy’s cycle, there are two ways of connecting
science with common sense: the direct, which we may call the “scien-
tific” one, and a second, which connects science with common sense
by means of metaphysics. In the scientific way, the statements of
science are interpreted by means of operational definitions as state-

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modern science and its philosophy

ments about observable facts, and every observable fact in physics can
be expressed in the language of common-sense experience.

Einstein’s statement that a rigid body has different lengths with
respect to different systems of reference can be connected with com-
mon-sense statements in two ways. We can describe directly the way in
which the length of one and the same rigid body can be measured by
putting end to end yardsticks that have different velocities relative to
the body. In contrast to this scientific connection, the metaphysical
interpretation would be: the statement that “one and the same length
is estimated differently by different observers” reminds us of the ex-
perience of everyday life that one and the same length is estimated
differently by different observers. This “subjectivity” of every judgment
about length seems analogous to Einstein’s contention that the length
depends on the .system of reference. Therefore, Einstein’s statement is
interpreted as claiming the “subjectivity” of human statements about
length. This is again in line with some statements of idealistic
philosophy.

We also find similar views in writings of other philosophers of
scientific background. I mention A. N. Whitehead, C. S. Peirce, and
in particular, a Thomistic philosopher, H. V, Gill. He regards the meta-
physical interpretation, as many people do, as a result of “intuition.”
But he realizes somehow that it is actually an application of common-
sense judgment to the principles of science. He noticed that the
scientists (he calls them “specialists”) will not do as well in finding
these interpretations as the “man in the street” who relies on common
sense only. Gill says; ®

The fact that a few “specialists” call in question some intuition generally
accepted by men does not furnish a valid reason for doubting its truth. The
specialist is indeed perhaps the one whose view on first principles should be
taken most cautiously.

The metaphysical interpretation is actually a particular kind of
^ semantic approach; it is a translation into common-sense language.
We follow Gharles Morris’s excellent analysis of the "metaphysical

*■ * H. V. Gill, Fact and Fiction in Modem Science (Dublin: Gill, 1943), p. 21.

logic and metaphysics in modern science

discourse.” ’ It is a “formative discourse” like the mathematical, logical,
grammatical and rhetorical discourse. A criterion of truth (similar to
the criterion of “scientific truth”) cannot be applied. The metaphysical
discourse plays a role in organizing human behavior and has, therefore, ^
“significance.” The present paper means to be more specific and to
describe the language used in metaphysics as the result of an attempt
to interpret the general laws of science by using common-sense ex-
pressions. The “materialistic” and “idealistic” interpretations of science
owe their appeal to the common-sense meaning of the words “matter” ^
and “mind” and not to their scientific meaning, which can hardly be
stated precisely.

From these considerations we can easily derive a sound judgment
about the role of metaphysics in the actual advance of science. What
we call in a vague way “common sense” is actually an older system of
science which was dropped because new discoveries demanded a new
conceptual scheme, a new language of science. Therefore the attempt
to interpret scientific principles by “common sense” means actually an
attempt to formulate our actual science by the conceptual scheme that
was adequate to an older stage of science, now abandoned.

According to these considerations, one can easily estimate what the
role of metaphysics in the advance of science has been. To believe that
some “metaphysical interpretation” may tell us the “truth” about the
“real world” means in practice to believe that the conceptual scheme of
some older stage of science is necessarily the scheme to be used for all
the future. This belief is, certainly, in a way stimulating: it encourages
the scientists in their attempt to stick to a unified scheme into which
every new discovery has to be fitted or perhaps even squeezed. To
achieve a unified scheme in all fields of physics is certainly a goal
that has been occasionally of great heuristic value. The most prominent
example is, I think, the attempt to interpret all physical phenomena by
Newton’s laws of motion. This attempt has led to great successes in
optics; we owe to it the corpuscular theory of light as well as the wave
theory. We owe to it almost all atomistic theories in their first stages.

*C. Morris, Signs, Language and Behavior (New York: Prentice-Hall, 1946),
pp. 175 ff.

301

modern science and its philosophy

But toward the end of the nineteenth century the physicists came more
and more to recognize that there are phenomena which can be fitted
into this “mechanistic” pattern only very artificially and incompletely.
Hence the heuristic value of this “mechanistic” goal faded as time
went on. Nevertheless the belief remained that only physical theories
which can be derived from Newton s laws of motion satisfy human
desire for “understanding” nature. In this stage this belief became a
purely metaphysical creed. Some maintained, for example, that Ein-
stein s modification of Newton’s laws had to be rejected for meta-
physical reasons. This actually means only that Einstein’s mechanics
cannot be derived from Newton’s laws of motion. It is a historic fact
that a great many physicists preferred to say that they rejected rela-
tivistic mechanics not for metaphysical reasons but for reasons of
“common sense.” Both types of reason for rejecting new physical
theories, as the argument in this paper shows, are really one and the
same thing expressed in two different ways.

The rationalistic metaphysician rejected new theories on die
ground of “reason,” the empiricist-metaphysician rejected them on the
basis of “common sense.” In my view, both types of rejection have a
common origin: the belief in the interpretation of new theories by using
the language of older theories.

Examples are abundant. I mention only cases in which “common
sense” prevented the acceptance of new physical theories, because the
scientists are more easily caught by “common sense” than by avowed
metaphysics.

The father of empiristic philosophy, Francis Bacon, rejected the
Copemican theory for not being in agreement with common sense;
the leader of nineteenth-century British empiricism, Herbert Spencer,
argued that the total mass of a system of material bodies cannot de-
pend on their distribution in space. August Comte, the father of
“positive philosophy,” predicted that no mathematical theory of
chemical phenomena will ever be advanced because our common sense
tells us that the chemical processes are fundamentally different from
physical processes. If we consider to what degree all these predictions
have been refuted by the actual advance of science, we can learn two

302

logic and metaphysics in modern science

things: metaphysics has very often been an obstacle to the advance of
science, and second, if we hear today that biology will never become
a science in the sense that mathematical physics is, or that sociology
can never use scientific methods, we shall hesitate in maintaining a
smug belief in these assertions.

303

BIBLIOGRAPHICAL NOTE

The essays in this volume have appeared in the following journals:

1. “Kausalgesetz und Erfahrung,” Ostwald’s Annden der NaUirphtbso-
phie 6, 443 (Leipzig, 1907).

2. “Die Bedeutung der physikalischen Erkenntnistheorie Machs fur das
Geistesleben der Gegenwart,” Naturtcissemchaften 5, 65 (Berlin, 1917).

3. “Ernst Mach— the centenary of his birth,” Erkerintnis 7, 247 (The
Hague, 1938).

4. “Was bedeulen die gegenwartigen physikalischen Theorien fiir die
allgemeine Erkermtnislehre?” Efkenntnis 1, 126 (Leipzig, 1930).

5. “La physique contemporaine manifeste-t-elle une tendence a r6int6grer
un 616ment psychique?” Revue de synthdse 8, 133 (Paris, 1934).

6 and 10. "The mechanical versus the mathematical conception of nature,”
Philosophy of Science 4, 41 (1937).

7. “Modern physics and common sense,” Scripta MathemaHca 6, No. 1
(1939).

8. “Die philosophischen Missdeutungen der Quantentheorie,” Erkennt-
nis (Leipzig, 1936).

9. “Bemerkungen zu E. Cassirer: Determinismus und Indeterminismus
in der modemen Physik,” Theoria 4, 70 (Gbteborg, 1938).

11. “Logisierender Empirismus in der Philosophie der U.S.S.R.,” Actes du
Congris International de PhUosophie Sdentifique (Paris, 1936).

12. “Why do scientists and philosophers so often disagree about the
merits of a new theory?” Reviews of Modem Physics 13, 171 ( 1941) .

13. “The philosophical meaning of the Copernican revolution,” Proceed-
ings of the American PhUosophicd Society 87, 381 (1944).

14. "The place of the philosophy of science in the curriculum of the
physics student,” American Journal of Physics 15, 202 (1947).

15. “Science teaching and the humanities,” Etc.: A Review of General
Semantics 4, 3 ( 1946) .

16. “The place of logic and metaphysics in the advancement of modem
science,” Philosophy of Science 15, 275 (1947).

Chapters 1, 2, 3, 4, 5, 8, 9, and 11 also appeared in Between Physics
and Philosophy (Harvard University Press, 1941).

INDEX

Acceleiation, operational meaning of,
236, 245

Accuracy, arbitrary, 117
Action, procedures of, 5; existence of
quantum of, 108, 110; spontaneity of,
162; objective observation of human,
166; at a distance, 211
Adler, Mortimer J., 271
Age of Enlightenment, 72, 74, 280
Age of Galiko, 122
Age of Newton, 122
Agnosticism, 14; Mach accused of, 17
Agreement, of physical theory with ob-
servations and principles, 210
Alembert. Jean Le Rond d’, 75
America, 216

Analogy, representation by, 150; to or-
ganism or mechanism, 252; tradi-
tional, 253; universe intelligible by,
298

Analysis, logico-empirical, 245, 253;
semantic, 245, 249; socio-psychologic,
249; pragmatic, 249; historical, 278
Analysis of Sensations, The (Mach),
69, 81

Angels, behavior of, 271
Animism, rejection of medieval, 140; in
Newton’s conception of force, 224
Animistic science, return to, 194
Anschaulich, 147
Anschamng, 147, 197
Approach, coherent, 250; socio-psycho-
logic, 250; semantic, 300
Approximations, successive, 118
Aquinas, St. Thomas, 219, 220, 221,
223, 251, 271, 284, 286
Arbitrariness, 266

Argument, philosophic and historical,
276; epistemological, 296
Aristotelianism, 73, 281; fundamentalist
and modernist attitudes, 23-24

Aristotle, 23, 37, 103, 115, 218, 284,
287

Arrangements, complementary, 163
Art, as personal experience, 42
Assertion, idealistic, 112
Assignment, rules of, 120
Astronomical instruments, 146
Astronomy, 271; Greek, 23; no true, 225
Atom(s), 67; concept of, a fiction, 43;
electrons and, 66, 116; no longer rigid
lumps of reality, 188; dematerializa-
tion, 190

Atomic bomb, 262
Atomic energy, 254
Atomic processes, laws of, 125
Atomism, 143; mechanical, 58; aversion
of Mach and Duhem for, 140
Atomistics, 65, 76, 116, 117; Mach's
opposition to, 70
Attitude, complacent, 279
Austria, 18, 26
Avenoes, 221, 224

Axioms, 242; arbitrary, 12; of coordina-
tion, 31; of geometry, 134, 244; of
parallels, 134; self-evident, 254; of
Newtonian mechanics, 270. See dso
Structural system
Ayer, A. J., 48

Background, cultural, philosophy of sci-
ence and, 42

Bacon, Francis, 209, 210, 232, 302
Balmer series, 107
Bavink, Bernard, 123, 125, 187-189
Beast of prey, philosophical, 76
Beauty, requirements of, 296
Becker, Carl, 286-289
Behaviorism, 166

Being, kinds of, 37 , ^

Bergson, Henri, 95, 101, 115

307

index

Berlceley, Bishop George, 85, 193, 199,

201, 210

Bible, cntenon of fruits, 64, as scaentific
textbook, 74
Biological advantage, 65
Biological-pragmatic approach, to sci-
entific conception of nature, 110
Biology, 84, concepts of, 37, evolution-
ary, 103, antimechanical, 125, vital-
istic, 159, understanding of, in terms
of physics, 165, Bohr’s thought m,
170, application of complementary
prmciple to, 180
Biophysics, 273
Blumberg, A , 38

Bodies, properties of, 56, 58, movement
of tvo, 104, rigid, 107, 136, of aver-
age size with moderate velocities,
131, of everyday experience, 153, ter-
restrial and celesbal, 221, moving,
contraction of, 226, problem of three,
235, material, existence of, 270
Body, "real” length of, 96, test, 117,
gulf between mmd and, 122, physical
causalitv m human, 166
Bohr, Niels, 179, principle of comple-
mentarit), 15^159, 163, 165, 166,
170, 182, 240, 246 255, 275, theory
of hydrogen atom, 291
Boll, Marcel, 48

Boltzmann, Ludwig, 141, 142, 150, 250
Bolyai. J4nos, 270
Bourgeoisie, 200
Bndges, logical, 173
Bridgman, P W , 20, 246, 250, 254,
256, 293, theory of meaning, 44-45,
224, 225, 244, 247, 253
Brvson, Lyman, 52
Burtt, 224

Calculus, differential, 135, 194
Cambridge, England, 49
Cambridge, Massachusetts, 49
Canossa, scientist’s trip to, 92
Carnap, Rudolf, 37, 38, 41, 44, 45, 48,
84, 85, 161, 166, 171, 202, 256,
philosophical system, 33-36, 86, 111-
112, 121, 152, 162
^artesian system, 236-238
Cartesians, 132

Cash value, meaning as, 32, 33
Cassuer, Ernst, 24, 172, 17^183 pasnm
Categories, theoiy of, 9
Catliolic Church See Homan Church
Catholic colleges, 256
Catholicism, Duhem’s belief m, 16
Causality, 112, concept of, 115, 255,
discussions of, 207, framework of,
120, law of, 10-11, 53-60, 175, 176,
270, as arbitrary convenbon, 14, es-
tablishment of a terminology, 57,
Kant’s formulabon, 177, validity or
nonvalidity, 117—118, physical, in hu-
man body, 166, strict, 119
Causes, mechanical and orgamc, 4, real,
46, my sbcal vital, 96
Celesbal bodies, 221
Cenbal Europe, movement toward sci-
entific world conception, 26, 44
Centrifugal force, 225
Changes, speculative, 113
Chemist, professional, 232
Chemistry, classes m, 232
Chicago, University of, 48
Chnstoffel, Elwin Bruno, 134, 135, 136
Churchman, C West, 42
Circles, eccenbic, 221
Civilizabon, technical, 122, cause of,
260

Clarity, lack of, in termmology, 164
Clirke, Samuel, 132
Classes, science, 243
Clavius, C , 208
Clergymen, 263
Climate of opinion, 287
Clockwork, understandmg of, 211
Coefficients, Fourier, 292
Cognition, 113, Schlick’s theory of, 29-
30, 42

Cohen, Hermann, 194
Colonng, emofaonal, 173
Colors, Goethe’s doebme of, 70
Columbia University, 48
Columbus, Christopher, 101, 108, 216
Common sense, 209, 232, 240, 252, 279,
289, m mterpretation of experiments
97, contradicbon to, 144, accordance
with, 156, and pnnciples of science,
289, 300, criteria of, 290, require-
ments of, 296, departure of science
from, 299, m mteipretabon of laws

308

index

of science, 301; an older system of
science, 301

Common-sense conception, untutored
man’s, 184

Common-sense method, Galileo’s, 286
Common-sense statements, 300
Communism, 191, 263. See also Soviet
Union

Communist revolution, 201
Comparison, role of, in physics, 298
Complementarity concept, 162-166
passim, 182, 240, 246, 255, 275; lack
of argument for free will, 170
Complexes of perceptions, 80
Compton effect, 117, 169
Computations, matliematical, 267
Comte, Auguste, 14, 290; positive phi-
losophy of, 9, 12, 166, 256, 302; defi-
nition of philosophy, 37
Conant, James B., 50
Concepts, geometric, 12-13; auxiliary,
18, 67, 73, 74. 99, 174-175; observa-
tional and auxiliary, 27-28; abstract
and of observational, 30-31; meta-
physical, 37, 83; theologic, 74; eight-
eenth-century, 76; constitution of,
111; mathematical, 135
Conclusion, logical, 242, 289
Confirmation, degree of, 28, 288; ex-
perimental, mathematical proof and,
234

Conscience, voice of, 277
Consequences, agreement of, with ob-
servations, 210

“Conservation of Energy’’ (Helmholtz),
213

Conventionalism, 11, 100-101, 176
Conventionalistic assertion, 176
Conventions, laws of science as, 10-
11

Cooperation, organization of interna-
tional, 49
Coordinates, 236

Coordination, axioms of, 31; relations of,
44; rules of, 245
Copenhagen, 49, 179
Copemican world system, 90-91, 216-
227; conflict with Roman Church, 16,
47, 218, 226, 232, 268; attitude of
scientists and philosophers toward,
207

Copernicus, Nicholas, 63, 73, 90, 144,
210, 214, 216-227 passim, 268, 284
Corpuscular theory, 246
Correlations, epistemological, 244
Correspondence, unique, 29, 105;

Schlick’s theory of cognition as es-
tablishment of, 29-30
Cosmological problems, 237
Courses, 232; elementary science, 249;

survey, for advanced students, M4
Creeds, metaphysical, 46; political and
religious, 46, 258, 281
Criminal, responsibility of, 167
Criticism, immanent, 172; scholastic,
173

Critique of Pure Reasort (Kant), 57
Crystal lattice, 113
Curriculum, college, 51
Czechoslovakia, 18, 26, 39, 45

Defeatism, attitude of, 269
Definitions, operation^, 20, 22, 28, 44,
244, 253, 278, 291; conventional, 53,
54; disguised, 57, 100
Demagogues, 266
Demiurge, creations of, 133
Democracy, fight against liberalism and,
280

Democritus, 58, 196, 211
Descartes, Ren4, 211; issues between
Newton and, 279

Description(s), Mach’s view of explana-
tion and, 6-7; Duhem’s theory, 16;
simplest, 65; theories as pure, 143;
space-time and causal, 164; comple-
mentary, 164, 167; classical and
quantum-mechanical, 170; of physical
devices, 267; direct and indirect, 297
Determinism, 46; strict, 96; philosophic,
176; concept of, 255; overthrow of
physical, 282
Deterministic laws, 176
Deterministic postulate, 177
Deviations, idealistic, 203
Dewey, John, 256
Dialectical Materialism, 191
Dialectics, trivialization of, 202
Diamat. See Materialism, dialectical
Differential equations, 130, 143
Dingier, Hugo, 101
Dirac, P. A. M., 179

309

Index

Discourse, metaphysical, 46, 290, 300-
301

Disputes, of metaphysical character, 152
Dnieprostroy, 201

Doctrines, traditional, and school philos-
ophy, 40; medieval, 122; physical,
philosophic and religious implications,
263

Driesch, Hans, 53-54, 57-60 passim
Du Bois-Reymond, Emil, 92-93, 97, 213
Duhem, Pierre, 14, 17, 20, 30, 49, 100,
140, 178, 257; physical theories, 15-
17, 21, 25, 04

Earth, mobility of, 222; influence of ro-
tation of, 237
Eccentrics, 219, 222
Economy, Mach principle of, 63; capi-
talist, 126

Eddington, Sir Arthur Stanley, 130, 243,
257, 296

Education, general, 233, 261, 262, 271,-
specialization versus general, 261, 273
Ehrenhaft, F., 71

Eighteenth century, 212, 281; Mach’s
nostalgia for, 72; spirit of, 224
Einstein, Albert, 124, 136, 180, 210,
234, 263, 295, 296; on law of causal-
ity, 10-11; relativity theory, 18-21,
26, 68, 73-74, 127, 131, 225, 229,
275, 291; lecture on “Geometry and
Experience,” 22-23; integration into
new positivism, 28, 44, 48; physics
of, 130; theory of gravitation, 134-
135, 227; conflict with Newtonians,
268, 270; Herbert Spencer Lecture,
294, 297

Einstein time scale, 113
Einsteinian revolution, 216, 225
Electric field, measuring intensity of,
117

Electric forces, as elements of reality, 27
Electric intensities, 59, 115
Electrical phenomena, true cognition of,
106

Electricity, 58; nature of, 93, 98
Electromagnetic field, Maxwell's, 140,
239

Electromagnetic mass, 161
Electrons, 67; atoms and, 60; coinci-

dence between, 116; light diffracted
or scattered by, 116, 118; personifica-
tion of, 118; positions and velocities
of, 118

Elements, intuitional, 27
Emerson, Ralph Waldo, 228, 232
Empathic understanding, 197
Empirical Philosophy, Society for, 40
Empirical tests, 147

Empiricism, 251; logical, 16, 45-49,
85, 86, 173, 175, 180, 197, 203; Eng-
lish, 195; positivistic, superiority of
mechanism, 196; crawling, 198; ad-
vocate of, 209; crude, 265
Empiricist, pure, 97
Empiricist-metaphysician, 302
Energetics, 58, 137, 158
Energy, conservation of, 53, 164, 220,
266; matter and, 66; minimum of dif-
ferent kinds, 71; degradation of, 123;
concept of, 255; disappearance of,
298

Energy transformations, phenomena as,
158

Engels, Friedrich, 202, 257, 266
England: See Great Britain
Ennghtenment, Mach as philosopher of,
17-18; philosophy of, 72-78; spear-
head of, 267
Entelechy, 59, 60
Entities, metaphysical, 18
Entity, Neurams avoidance of word,
35

Epicureans, 281; materialism of, 132
Epicycles, 219, 221, 222
Epistemological foundation, 70
Episteraologist, 91

“Epistemology of the Exact Sciences,”
40

Equations, field, 113, 140; differentia],
130, 143; Newton’s, 242
Equivalence, principles of, in Einstein’s
theory, 18

Erkennfnis, mouthpiece of Vienna
group, 41

Ernst Mach and Marxism (Valentinov),
190

Ernst Mach Association, 40
Essence, Neurath’s avoidance of word,
35

Essential, misinterpretation of word, 35

310

index

ETC.. A Review of Genet d Semantia,
247

Ether, matter-like, 153 Ntlocity with
respect to the, 154, 155
Ethics, 24, 277, eudacmonistic, and pos-
itivistic sociology, 39, relation to
quantum mechanics, 184, absolute
\ allies of, 230 factois of, 255, syn-
thesis with science, politics, and reli-
gion, 271

Euclid, 12-13, axioms of c oordinaboii,
31

rxistcncc, real, lOS, of external objects,
268

Lxpcncncc(s), Kant’s theory of, 7 8,
objectnc, and mind, 9, leisoning and,
in geometrj, 21-23, dcsiie for pei-
sonal, 42, science as economical rcp-
lesentation of, 84, unequisocal as-
signment of s)mbols to, 106, concrete,
similarity between. 111, real, 118,
correspondence betw een symbols and,
118-119, point, 119, everydav, 145,
149, 152, 288, naive sense, 217, 218
Experiments, world of physical, 243
Experimeutum cruets, 15
Explanation, scientific and mechanical,
6, Duhem’s theory of, 16, mecha-
nistic, 138-140, causal, 211, plqsical,
226

Explanatory \ alue, of mechanistic theo-
ries, 139

Exposition, emotional undertone of, 174

ract(s), obserxed, in Mach’s theory of
science, 11, obserx ational, Einstein’s
tlicory in terms of, 19, 20, economical
dtsciiption of, 20-21 xxorld of, 42
objectixe, 80, 127, 128 statement
about obseiyed, 242, confirmable,
266, marriage of reason and, 286
Factors, extrascientific, 283
Faith, matters of, 130
Farada) , Michael, lines of force, 63
ratadat/s Lines of Fotce (Maxwell),
141

Fascism, 266, 282
Feeling, optimistic, 42
Feigl, H , 38

Feudalism, return to ideas of, 282
Fictions, mathematical, 91

Field equations, integration of, 113,
Maxwell’s, 139-140
Field intensities, 115
Finkelstein, Louis, 52
Fislce, John, 257
Fluid vortices, 132
Fog, enigmatic, 229
Force, Faraday’s lines of, 63, concept
of, 80, 247, nature of, 93, 99
Formal idiom, 152

Formulas, matliematical, 46, 138, physi-
cal meaning of, 267

Fonnulations, sensible and meaningless,
of problems, 95, metaphysical, 164
Fossihzation, 208
Foul dimensional space, 152, 158
Fouiier coefficients of radiation, 292
Frame of reference, 154
Framcyxork, man’s, in cribcal idealism,
58, rigid, of space, tune, and causal-
ity, 120

France, materialism in, 125
Frankenstein’s monster, 283
Free will, 159, 162, 166, 183, science
and, 125, not an eipression from
psychology, 167, belief m, 230
Freedom, from intoxication and hypno-
sis, 167, from external coercion, 167,
itlucal, 183 real and pseudo, 238
Fiege, 103

French, peciiliai ties of, 148
Flench Rexolution, 124, 216, 281
Fruits, criterion of, 64, of Mach’s teach-
ings, 68

Galactic s\ stem, 226
Galaxies 237

Galileo 90, 159 186, 214, 223, 286,
287 dialogues of, 73, trial of, 91,
physics of, 115, 123, 138
GaJvanometer, 107
Gauss, Karl Friedrich, 270
General Education Program, Harvard
Umxersity, 50

Generalizations, popular, 274
Geoccntiic system, 146, 208, 218, 222,
225

Geodesics, 130
Geometnc imagery, 151
Geometric theorem, 233 • ,

Geometry, 242, 243, Euclidean, 8, 9,

311

index

12-13, 21-24 paisim, 91, 114, 134,
147, 270, non-Eudidean, 8, 9, 21-

22, 91, 147, 233, 234, 254, 270, foun-
dahons of, 13, 234, 239, 240, 241,
245, reasoning and experience m 21-

23, Rcichenbach’s conception of, 31,
Kicnunnian, 136, iinderstanding of,
235, axioms of, 244, logico-empirical
analysis of, 253, niathcmatiLal, 253,
semantic analysis of, 254

“Geometry and CxpericiiLc” (Einstein),
22, 245

German Plixsital Soc.ict\. 39-10
German), 124, Weimar expenment, 26
unixersities of, 31, niittnalism in,
125 Na7i. 195
Gill, H V , 300

God, 222, science and, 125, \xill of, 277
Goethe, Johann Wolfgang \on, 62-63,
doctiinc ol colors, 70, extreme phe-
nomalist, 71
Good life, 272
Good xmII, 279

Government, relations between science,
religion and, 232

Gravitation, 123 theory of, 135, law of,
210, 211, 212, 214, 217, Einstein’s
till orv of, 227

Gravitational field, Einstein’s laws of, 18
Great Britain, 48, 50, analytic and spec-
ulative philosophy in, 36
Groups, totalitarian. 34

Iladamard, J , 295
Hahn, Hans, 1, 31 32, 33, 34, 38
Hardness, meisiircment of, 114
Harvard Observatorv, 226
Harvard Umversitv, 48, 49, 50, 250
Havakavva, S 1 , 247
Heavens, real motions of 222
Hegrl, G W r , 88, 202, 284, objective
idealism of, 201

I Ii gtlianism, idealistic eggshell of, 203
Heisenberg, Werner, 116, 127, 179, 291,
292, principle of uncertainty, 168,
240, 275

Heliocentric theory, 144-146, 218, 225
Helmholtz, H L F von, 134, 136, 138,
213

Herbert Spencer Lecture, 294, 297
Hermann, Crete, 177, 184

Hertz, lleiniieh, 93, 140, 141
Heuristic principle, 294
High frequencies, 117
Hilbert, David, new foundations of ge-
ometry, 13 103
Ihllebrand, K , 195-197
History, 276, of science, 149, courses m,
232, of British kings, 233, laws of,
271

Holism, 195
Human interest, 232
Human society, crisis in, 136
Huniaiiitics, 232 stienct and, 258, 261,
281, 284, basis of education, 260, m-
Icicst 111 , 278, instruction in, 283
Hume, David, 12, II 242, 256, law of
causality, 10

Ilinghens, Christian 138
Ilvdrogcn atom, Bohi’s tlieoiy ol, 291
Ilvpotheses, as ‘ciffolds, 62, niinimum
of, 71, phssical, 214, petrifaction of,
214 working, 220 not articles of
filth 220

lIi/pothest% non fingo, 138, 211

Idevhsm, 35, 81, 85 91 201, 257, rela-
tion to positivism, 11, subjective, 14,
193, 201 German 47, critical, 58,
antithesis to m iteiialism, 85-86,
movement toward, in modern physics,
120-137, 192, transcendental, 174,
182 propaganda for, 190, objective,
of Hegel, 201, mcnshevizing, 203,
two front war agiinst, 206, varieties
of Kaiiti in, 257
Idcilistic asscition, 112
Idealists. 95, problem of materialists
and 30

Ideas, general, prejudice against, 273
Ideologies, 258, 283, conflict of politi-
cal, with science, 17, of new organ-
ismic state, 126, antiscientific, 230,
historical and contemporary, 258, ri-
val, struggle among, 281
Ignorabimus, 92-95 passim, 97, 99, 111,
112

Ignonng the facts, 264
Imagery, geometric, 151
Imagination, 266, free, axiomatic sys-
tem a product of, 14, human, 58, 60,
logical, 297

312

index

Indeterminacy, principle of, 255
Indeterminism, concept of, 255
Indoctrination, political and religious,
273

Induction, law of, 270
Inertia, law of, 53, 210, 212, 214, 235-
236

Inquisition, 91; condemnation of Co-
pemican system, 208
Integration, philosophy of, 36-37
Intelligentsia, middle-class, 191
Intensities, electric and magnetic field,

59, 115

Interlude, Kantian, 47
Interpretations, metaphysical, 51, 164,
300; philosophic, 159; pseudophilo-
sophic and pseudoreligious, 231; logi-
co-empirical, 290
Interpreters, philosophic, 168
Intersection, geometric concept of, 12,

Intervention, of political powers, 51
Intolerance, spirit of, 279
Intuition, internal, 147-148
Intuitive theory, 150-151
Iron curtain, between science and phi-
losophy, 25

Irony of embarrassment, 114
Issues, historic, 282
Italy, 124

James, William, 32, 33, 40, 79, 95, 101-
103, 111, 218, 256
Jaumann, Gustav, 71
jeans. Sir James, 129, 130, 133, 134,
135, 184, 186, 188, 250
Jesuit, 209
Jordan, P., 184

Journal, philosophical, of Vienna Cir-
cle, 38

Journal for the Whole of the Natural
Sciences, 195

Judgment(s), subject-predicate form of,
104; relation of true, to reality, 105
Jupiter, planet, 223

Kant, Immanuel, 23, 95, 147, 180, 212,
214, 257; theory of knowledge, 7;
conception of geometry and me-
chanics, 7-8; idealistic philosophy, 9,

11; Critique of Pure Reason, 57; for-

3T3

mulation of law of causality, 175, 177
Kantian interlude, 47
Kantianism, 40, 47; fundamentalist and
modern attitudes, 23-24; new philos-
ophy and, 31. See also Neo-Kantian-
ism

Kepler, Joliannes, 63, 90
Kirehhoff, Gustav Robert, 65
Kleinpeter, H., 77

Knowledge, 233; theory of, 7, 90; syn-
thesis of, 88, 262, 271; limits of,
9.3; cxtrasL-ientific or superscientific
sources of, 193; explanatory and un-
derstanding, 196; genuinely satisfy-
ing, 196; integration of, 230, 271,
276; prescientific, 268, 270; isolated
branches of, 269; beyond science,
269; useful, without truth, 271
Kronecker, Leopold, 66, 67

Labor, division of, 37, 260; problems,
247

Lacunae, in science for introduction of
supernatural factors, 183
Lange, F. A., 194

Language, phenomenal, 35, 85, 87, 171;
transition from quasi-idealistic to
quasi-materialistic, 36; physicalistic,
36, 161, 202; of unified science, 37,
87; Mach’s perception, 83-84; physi-
cal, of Neurath, 85, 87; formative
rules of, 154; of daily affairs, 157,
171, 179; of quantum physics, 157;
universal, of science, 161; comple-
mentary, 166; protocol, 171; symbol,
of psychoanalysis, 171; intersubjec-
tive, 202; kitchen, 243
Laplace, Pierre Simon de, 124, 175,
177; school of, 281

Law(s), physical, 6, 149; statistical,
119; deterministic, 176; concept of,
178; metaphysical, 264
Law of Causality and Its Limits, The
(Frank), 176
Leaves, withered, 64
Leibniz, Gottfried Wilhelm von, 47,
132, 138; Newton and, 280
Length, measurement of, 115-117; op-
tical illusion of, 127; relative and ab-
solute, 154-155, 239, 246; subjectiv-
ity of statements about, 300

index

‘‘Length of a lod,” 127
Lenin, Nikolai, 10, 11, 100, 125, 190,
191, 193, 198-199, 204, 258, 284,
denunciation of \lachism, 17, 35,
47

Le Roy, E , 299

Lessing, Gotthold Ephraim, attacks on
Voltaire, 72

Levi-Ci\ita, Tullio, 134, 135
Liberalism, fight against democracy
and, 280-281

Life, 83, conscious intellectual, 159,
Mtalistic conception of, 159
Light, nature of, 93, 98, identity with
electromagnetic radiation, 98, dif-
fr.icted oi scattered by electrons,
116, waselengtli of, 116, corpuscular
theory of, 211, wase theory of, 246
Light quanta, 116, 117
Light rays, 107

Limitations, absence of, in changes in
symbol system, 113-114
"Limitations of Natural Science” (Du
Bois Reymond), 92
Literature, courses in, 232
Lobatchevski, Nikolai IvanoMch, 270
Logic, need of pragmatic oil, 11, sym-
bolic, 31, 39, 44 formal, role of, 103,
of school philosophv, 103-104, Aris-
totelian, 104, modem, 110, shift in
the place of, 286, decline of, 1 1 twen-
tietli century, 287, in ad\ aiice of
tweiitietli-century science, 296, place
of, 297

“Logical positivism” (Blumberg and
Feigl), 38

Logical Syntax of Language, The
(Cainap), 86

Logico-empirical interpretation, 290
Logistics, a formalistic game, 205
Longing, unfulfilled, 159
Loops, traced by planets, 217
Lorentz, H A , 59
Lutheran tlieologian, 219
Lyric poetry, 112

Mach, Ernst, 32, 46, 110, 140, 141, 250,
252, 256, 298, conception of explana-
tion, G, antimetaphysical tendencies,
7, cnbcism of New ton’s mechanics, 8

theory oi general piinciplcs of sci-
ence, 11, integration with Fomcaiu
and Einstein, 11-15, 33, 44, Soviet
attack on, 17, 35, 47, philosophy of,
17-18, 35, 37, 72-89, 99-100, 102-
103, 121, 224, 225, 265, 291, 297,
fascination of teacliings, 61, position
of, in contemporary intellectual life,
61-67, value of doctrines, 67-72, fol-
lowers of, 192, 198, positivistic re-
quirement, 294

Machism, 66, 198 denounced by Lenin,
17, 35, 47, niclaphvsically conceived,
194

Magazines, populai science, 230
Magnetic field mtcnsitiis, 59
Magnetism, 58

Maimonedes, Mo‘cs, 221-222
Man, primiti' c, world picture of, 80
Man-in-the-strect, 156, 268, 300
Mankind, presiientific cvpericiicc of,
269

Marburg, nco-Kaiitian school of, 194
Mantain, Jacques, 24, 175, 297-298
Mus, planet, 229

Marx, Karl, 125, 202, 257, 266, 284
Maixism, 190, 272
Masar\ k, Thomas G , 45
Mass, real and apparent, 160, meta-
physical principle of, 161, electro-
magnetic, 161, concept of, 255
Matciial idiom, 152
M itcrialism, 74, 78, 81, 85, 190, 257,
258, 281, methodical, 35, dialectical,
47 88, 125, 160, 198, 203, 204, 257,
258, 271, 273, 273, 283, struggle
against, 80, antithesis to idealism,
85-86, in Germany and France, 125,
dangers for, 191, strictly taboo, 193,
metaphysically conceived, 194, mech-
anistic, 201, 257, political systems
based on, 263, refutation of, 280
Materuihsm and Empinocnhcam
(Lenin), 11, 190, 193
Materialists, problem of idealists and,
30, false philosophy of, 132, appre-
hensions of, 186, scientifically
mmded, 194

Mathematical Pnnctplei of Natural
Phdosophy (Newton), 212
Mathematically true, 214

314

index

Mathemabcians, meeting of physicists
and, Prague, 39-41, conception of
universe, 124.

Mathematics, foundations of, 31, 103,
spiiitual element, 123, 129, analytic
character of theorems, 134, pure,
propositions of, 134, concepts, 135,
fetish, 192, replacement of mechan-
ics, 192, relationship with physics,

194, 234, traditional teaching of, 253,
264, educational values intrinsic m,

271, creative principle in, 297
Matnces, Heisenberg’s, 292

Matter, 83, Neurath’s avoidance of
word, 35, and energy, 66, an auxil-
iary concept, 74, nature of, 93, 99,
electromagnetic picture of, 137, only
an illusion, 160, conception of,
changes hy electromagnetic theones,
190, disappears, 190
Maxwell, James Clerk, 63, 70, 139-142,
150, 239

Meaning, conception of, 32, 33, crite
non of, 44, 295, theories of, 44-43,
291, 292, definite, 154, deeper, 174
operational, 224, 225, 244, physical,
235

Meaninglessness, Bridgman’s concept of,
44

Measurement, of space and time in
Einstein’s theorv, 19, traditional sys-
tems of, 22, “correct,” 96, methods
of, 115-117, refinement of tech-
nique, 116, 120, role of obseivei,
127-128, physical, 243
Measuring tod, 116
Mech mica! engineering, 237
Mccli lines, Newtonian, 8, 9, 23, 73, 114,
136, 160, 213, 224, 239, 234, 270,

272, theological, animistic, and mys-
tical points of view in, 72, wave, 118,
131, classical .ind relativistic, 153,
155, replacement by mathematics
192, traditional college, 239, founda-
tions of, 240, 241, 245, laws of, 244,
Einsteinian, 272 See also Quantum
mechanics

Mechanics (Mach), 71-72, 82
Mechanism, question of vitalism or, 59,
60, breakdown of, into positivism,

195, superiority to positivistic em-

piricism, 196, Euclidean science, 196,
two-front war against, 206
Mechanistic scheme, 257
Mechanistic science See Science, niech-
anisbc

Mediterranean races, peculiarities of,
148

Medium, vibrations of, 120
Mental constitution, 151
Metaphysical systems, crude, 265
Metaphysician, rabonalisbc, 302
Metaphysics, 193, 238, 295, relabons to
science and religion, 15, Duhem’s dis-
bnction between physics and, 16,
Arivtotehan, 16, 24, Thomisbc, 16,
26, 298, traditional, 23, 34, 36, Kant-
ian, 24, 26, 47, statements of, as social
phenomena, 34, elimination of, 34-
35, 82-85, 89, Schhek’s view of, 41-
42, justification of, 42, idealistic, 86,
88, materialistic, 86, 159, impor-
tance of, to science, 87, spiritualisbc,
132, 159, critical attitude towaid,
181, scientific, 187, twentieth-cen-
tury tendency toward, 192, German
inclination toward, 212, sbaight, 256,
organismic, 258, dcclme of, 290, con-
cepbon of, 290, interpretation of
principles m terms of language of
everyday life, 290, heuristic value,
297, 298, characteristic of, 299, lan-
guage used in, 301

“Metaphysics of Modem Physics”
(Wen^l), 189
Methods, experimental, 42
Michelson’s experiment, 254
Middle Ages, 124, 186, 286, animistic
science of, 122-123, language of, 211
Milky Wav, 226, 237
Mill, John Stuart, 9, 12
Mind, nature of human, 7, ohjeebve ex-
peiience and, 9, fiee creabons of, m
Poincare’s theory of science, 12, Neu-
ratli’s avoidance of word, 35, eman-
cipation of, 69, gulf between body
and, 122, problem of explaining, 122,
creabvity of human, 278
Mismterpretabons, of physical theones,
46-47, philosophic, 160, metaphysi-
cal, 164, 165
Mitm, M , 191

315

index

Models, mechanical, 150, 152
Momentum, conservation of, 164.
Morris, Charles H , 48, 49, 290, 300
Motion, Newton’s laws of, 8, 9, 145,
235, positivistic doctrine of space and,
68, absolute velocities ot, 117, of
bodies of average size with moder-
ate velocities, 131, sunple 208, triple,
208, indestructibility ot, 212, abso-
lute, expenditure ot divine energv,
224, real and apparent, 238, essence
of, 270

Nagel, E , 48

Narrowness, mechanistic, 199
Nationality, 150

Natural laws, fuimulation of, 14, mali-
cious, 182

Natural Science on the Path to Re-
ligion (Baviiik), 123
Nature, simplicity of, 11, poitrayil of,
57, fictitious, 5S, empirical, 59, scho-
lastic conception of, 90 suirender of
scientific conception of, 97, scientific
conception of, 110, insidious hws of,
117, spintualistic conception of, 124

137, organismic conception of, 124,
processes of, mechanical and mathe-
matical bases, 130, new physical con-
ception of, 136, 159, existence of
sunple laws, 176, mathemitical con-
ception of, 188, idealistic philosophv
of, 188, mechanistic conception ot,
287

Nazism, 248, 263
Negabon of the negation, 202
Negativism, positivism not a, 68
Neo-Anstotehamsm, 23-25
Neo-Kantiamsm, 23-25, 43
Neo-Tliomism, 23-25, 270
Neo-Thomists, French, 48-49
Neurath, Otto, 1, 2, 31, 34, 38, 85, 86,
161, 166, 171, 202, index of pri-
hibited words, 35, unification of sci-
ence, 36-38, 39, 47
Newspapers, 230

Newton, Sir Isaac, 63, 73, 132, 135,
159, 186, 210, 211, 223, 286, prin-
ciples of mechanics, 23, physics of,
115, 138, antimatenahsbc tendency,

138, equations, 242, contemporaries.

254, popularization of, 263, issues
between Deseartes and, 279, Leibnu
and, 280

Newtonian, Newton not a faithful, 211
Newtonian laws, 8, 9, 145, 156, 213,
214, 223, 225, 235, 237, presentation
of, 254, results of evpenence of every-
diy life, 289

Newtonians, conflict with Einstein, 268
Nietzsche, Friedrich, 9, 18, 75, 76-78
Nineteenth century, 136, 212, 216, 220,
224 261, 280, 286, ph)sical research,
149

Nummahsm, 252
Noninteivention, pohej of, 269
Nordic r ice, 248, characteristics of. 1 13
Northrop F S C , 42-43, 244, 258
Numheis, iriitiunal, 66, 108, 109, 110,
nitiire of complex, 100, i itiuiiil, con-
vergent sequent e of, 109
Nurimberg, 219, 222
Nurse, 265

Objetl(s), agreement bitwtcii thought
and 98, psyehologieal. 111, physic il,
170

Obscurantism, souice of, 267
Obseivabon, 242, nme sensoi), 146,
objective, of human actions, 166
agreement of consequences with, 210,
sense, 218

Observ ational teims, v ..gueness of, 1 3

Observer, role of, 127-128, 254

Observing subject, 126

Occam, William of, 284

Oec im’s razor, 252

Ontology, 41

Oper itionism, Biidgman’s, 258
Optical illusion, 217, of length, 127
Optics, statements ot, 245
Oiganicism, 195, glorification of mech-
anistic physics by advocates of, 196
Organism, physical disturbances of, 168
Osi inder, Andreas, 219-220, 222
Overspeciah/ation, superficiality and,
259

Oxford, 294

Faiallels, axiom of, 134
Paralogisms of rationalism, 48
Fans, 49

316

Index

Particle ( 9 ), as term m atomic physics,
170, small, with large velocities, 119
Paul III, Pope, 222
Peirce, C S , 32, 48, 256, 300
Peiception terms, 84
Perceptions, sense, 68, comple\es ot, 80
Pcifection, spiritual, 161
Periodicals, 230
Persecution, political, 50
PetnfaePons, 214, of Newton’s physics,
215

Phenomena, true cognition of electrical,
106, understanding of, 138, electro-
magnetic, 139, as energy transforma-
tions, 158
Phenomenalism, 70

Philosophers, 253, professional, 76, task
of, 114, idealistic, 147, Geimaii pro-
fessional, 187, scholastic, 209, diser
gence in attitude of physicists and,
210, tvsentieth-eeiitury, 210
Philosophic schools, reactionary, 191
Philosophical journal ot Vienna Circle,
38

Philosophically false, 214, 215, 218, 226
Philosophically true, 219, 221, 225
Philosophy, 255, 276, Catholic, 2, sci-
ence and, 4-5, 25 121, 207, 262, 265,

266, 269, 273, 275, haditum.d, 14-15,
23, 25, 28-29, 32, 43, 81, 82. 85. 88,
idealisbc, 18, 33, 80, 85, 160, 162,
165, 300, fundamentalist and mod-
el nist, 23, 25. Ceiman, 34, 47, ana-
lytic and speculative, 36, of integra-
tion, 36-37, Comte's definition of, 37,
dislike of term by Vienna group, 38,
new, of Vienna group, 38-39, turn in,
41-12, Aristotelian, 73, 211, 219, 220,
mathematical principles of, 132
atomistic, 142, orthodox, 149, contro-
\ersial questions of, 158, Kantian,
180 official, 193, orgamsmic, re-
garded as Cermm, 195, empirical,
212, 232, 242, departments of, 262,

267, relation to physics, 263, popular,
265, chance, 265, 287, 268, 276, ob-
solete m socifil and political life, 266,

268, special field of, 267, 268, 273,
275, vuerage instruction in, 267, as
integration to human knowledge, 270,
traditional teaching of. 271, mter-

acbon with science and rehgion, 279
See also School philosophy, Soviet
Union, philosophy of
Philosophy of ‘As If (Vaihinger), 43
Physical law, Mach’s theory of, 6, new
types of, 149

Physical terms, meaning of, 44
Pliysical theories, conception of, 19,
misinterpretations of, 46-47, fossiliza-
tion of, 115, modern, standpoint of
school philosophy, 119, philosophical
mterpietation of, 160
Physicahsm, 35, 36, 85, 166
Physicalists, 160

Physicists, meeting of mathematicians
and, Prague, 39—41, poor training of,
in philosophy, 46, reactions of, to
modern theories, 97, theoretical, work
of, 1 13, stimulus to, 146, progressis e,
151, di\ ergeiice in atbtude of philoso-
phers and, 210, twentieth-centiuy,
226, named, 230, experimental, gul-
libility of, 231, failure of learned,
264, lack ol philosophy of physics
among, 266, average, 274
Physics, 76, 122, 140, anthropomorphic
conception of, 159, Aristotelian, 73,
208, 209, 215, 219, 222, 223, 252,
as church, 78, atomic 240, comple-
ment'’rity conception, 179, no longer
deterministic, 177, nuclear and, 238,
world of, 157, classical 114, 115, 120,
127, as extinct organism, 280, crisis
ot, 280, epistemology of, 119, college,
elementary courses, 284, common-
sense, 241, concepts of, 37, crisis of,
2, 136, 215, Duhem's distinction be-
tween metaphssics and, 16, educa-
tional values intrmsic in, 271, Ein-
stein’s non-Aristotelian, 74, estab-
lished prmciples of, 223, experimen-
tal, 44, graduates in, 264, influence
of philosophical creeds, 23, laws of
59, gaps in, 183, logico-empirical,
253, Mach’s news of, 6-8, mate-
rialistic end of, 137, idealistic ele-
ment inside, 104, mechanisUc asser-
tion of ontologic value, 2, concepts of,
18, decline of, 2-3, 252, 280, orig-
inal sin, 123, overestimation of, m
behalf of orgamsmic science, 195,

317

index

196, penod of, 251-232, medieval,
139, 221, Newtonian, 132, 215, 280,
Hint teenth-Lcntiirv 139, 282, Ein-
stein’s theory and, 20, nonmechaincal,
mathematical, 131, orgmismic dw-
mtegration of, 252, return to, 282,
place of, in human thought, 5-6,
poMtiMstic 140, as \ariety of subjec-
ti\c idealism, 193, relationships with
mathematics, 194, 234, philosophj,
263, psychology, 69, sociology, 272,
spiritualistic, 128, 159 teaching of,
230 if , 264, 267, textbooks, 264, 278
traditional, 232, tw entieth-century
114, 120, 149, 215, 217, 231, 252,
253, 263, 282, 287, histoiy ot, 292,
influence on human affairs, 264, inter-
pretition of, 50, 231, 296, language
of, 299, new logical techniques, 254,
rebirth of idealistic, 123-137, 140,
186, understanding of, 96, undti-
standing of, 233-234 S e aho Sci
ence

Phisiologi, 83
Pick, George, 72
Pictorial representation, 147
Picturil theory, 139, 147, 148
Picturization, 139, 147
Planck, Max, 62-70 pfissim, 76, 166,
250

Planck constant ii, 102, 107
Planetary orbits, perturbations of the,
145

Poetry, as personal experience, 42, lyric,
112

Poincare, Henri, 17, 26, 30, 46, 48, 53,
54, 69, 100, 250, 256, 299, new posi-
tivism, 8-12, 20-21, structural sys
tern m physical theory, 13-14, inte-
gration with Mach and Einstein, 14-
15, 33, 44

Point, geometric concept of, 12, 13
Point experiences, 119
Pointer readings, 107, 128, 243
Poland, 18, 26

Political ideologies, conflict with sci-
ence, 17

Political problems, understanding of,
232

Politicians, global, 263

Politics, 271, 277, factors of, 255,

slogans m, 266, syntliesis with sci-
ence, ethics, and religion, 271
Popper, Josef, 72
Popularizations, superficial, 268
Position! s), initial velocity and, of elec-
tron, 118, indefinite, 103, new syn-
tax for word, 179

Positivism, 223, 251, breakdown of
mechanism into, 195, cause of,
against metaphysics, 23, Central Eu-
ropean, 48, 49, conneebon witli uni-
ficabon of science, 37, dislike of term
b\ Vienna group, 38 evolution of, 38,
logical, 39, 42, 43, 50, 256, mistake
of, 196 new 24, 26, 34, 35, 47,
Einstein’s theory and, 18, 20-21, 28,
French advocates, 48, Hilbert’s con-
tiibubon to, 13, mtegrabon of philos-
ophy of Mach, 14, mergence with
Thomistic metaphysics, 16, of Poin-
care, 9-12, 13, spirit of, 5, 6, nine-
teenth cenbiry, 178, not a negativism,
68, relation to idealism, 11, straight,
256, Study’s view of, 65, the rape uti-
c il, of Wittgenstein, 32
Positivists, 252

Pragmitism, 33, 102, 111, 223, 256,
Amencin, 40, 48, 203, Central Euio
pc in ijositivism and, 48, truth-con-
cept of, 112

Piagmatim (Janies), 95, 101
Prague, 47, 49, 99, meeting of piiysicists
and mathematicians, 39-41, Univer-
sity of, 31, 45, 47, 99
Preachers, 263

dedicate, subject and, in school logic,
104

Prediction, of future processes, 177
Predilections, religious and political, 256
Pre-Gahlcan penod, 287
Prejudices, popular, 9, metaphysic il,
173, 240, obsolete, 264
Prescienhfic stuff, 269
Presentations, popular, 164
Presuppositions, 270
Principles, tautological tiansformations
of, 110, Newton’s, 122, metaphysical
209, plnlosophic, 214, 215, checked
by extrascientific metliods, 251
Probability, mathematical, not a physi-
cal reality, 187

318

Probability concept, spiritual factor, 158
Problems, metaphysical, cognition in so-
lution of, 30, verbal, of traditional
philosophy, 32, soluble m prmciple,
111, pseudo, 162

Processes, prediction of future, 177
Professionid training, 230
Propaganda groups, 264
Properties, perceptible and impercep-
tible, of bodies, 56

Proof, mathematical, and experimental
confirmabon, 234

Froposibons, tautological system of, 24,
metaphysical, 84, 88, meaningless
metaphysical, 165, isolated, 173
Protocol language, 171
Pseudo-idea, 212

Psychic factors, in interpretataon of
physics, 126

Psvchoanalysis, symbol language of, 171
Psychologic fact, 213
Psychological elements, in me isure-
ment, 127, 128

Psychology, 83, 84, 271, concepts of,
37, connection of, with physics, 69,
individual, ISO, understanding of, in
terms of ph)sics, 165, empincal, 170,
application of complementaiy prin-
ciple to, 180

“Psychology of Metaphysics” (Nietz-
sche), 77

Ptolemaic system, 73. 143, 220, 221
Ptolemy, 208, 218
Punishment, 167

Quacks, 240
Quanta, 67, 230
Quantities, observable, 107
Quantization laws, 240
Quantum hypothesis, 116
Quantum mechanics, 114, 115, 120, 125,
128, 131, 153, 163, 292, principles of,
96, philosophic misinterpretahons,
162, syntactic form in, 180, relation
to ethics 184

Quantum of action, real existence of,
108, 109, 110

Quantum physics, laws of, 149, lan-
guige of, 157

Qii intum theoiy, 40, 126, 127, 130, 140,
148, 210, 215, 240, 252, 255, 267,

268, creation of, 123, mdetennin-
ishc mterpretahon of, 128, research
on, 151, analogy of free will to,
166, posibvisbc concepbon of, 178,
metaphysical interpretabon of, 182,
253, misuse of, 184, irrabona] as-
pect, 246
Qume, W. V, 48

Race, 150, 195

Race relabons, problem of, 247
Radar, 262

Radiabon, 08, 107, 292
Rationalism, illusion of, 5, new and ba-
dibonal, 9, paralogisms of, 48,
French, 195
Rationalists, 74

Reactions, of physicists to modern theo-
ries, 97

Real, use of, is word, 35, 162
Realism, 17, 94
Realist, 95

Reality, 62, objective, 14-15, 29, physi-
cal, 18, 178, 215, 221, ontological, 18,
electric forces as elements of, 27,
Neurath s avoidance of word, 35,
symbolic logic and its application to,

39, hidden iii a nutshell, 98 re-
lation of bue judgment to, 105, metv-
physical, 108, iionmechanical, 129,
concrete, 136, dual, 165

Re.'soii(s), pure, 212, 214, psychologic,
248, extrascientiEc, 248, 253, 256,
257, marriage of fact and, 286, dt-
chne of, in twenbetli century, 287
Riasoiniig, experience and, in geoni
cUv, 21-23 speculative, 218
Recurrence of a state of a system, 14
Reference, system of, 227, 235, 254
Heichenbach, H , 26, 30-35 passim,

40, 41, 44, 47, 48, 112, 115, 245
Relabon(s}, relation of, 10, of cooidina-

bon, 44, bebveen two things, 104,
analogical, 290, umvocal, 290
Relativism, Mach accused of, 17, of
modern science, 52
Relativity, theory of, 18-21, 26, 40, 46,
68, 73-74, 96, 97, 114^128 passim,
131, 135, 140, 148, 150, 153, 155,
162, 191, 210, 215, 217, 225, 226.
238, 245, 252, 253, 266-268, 27<

index

275, misunderstanding of, 127, popu-
lar literature on, 127, laws of, 149,
teachmg of, 238-239, 240, restiicted
theory of, 254, theory of meaning
and, 291

"Relativity— a richer truth,” 52
Relativity boom, 229, 262
Religion, 24, 193, 272, 277, relations
to science and metaphysics, 15, re-
lations with science, 17, 123, 230,
259, scientific world conception and,
40, mi\ing of, into science, 224, re-
lations between science, goienimenl,
and, 232. factors of, 255, ssnthesis
of science, ethics, politics, ind, 271,
interaction with science and philoso-
phy, 279

Representation, pictural, 139
Research, spirit of, 63, e\act scientific,
restricted to dead matter, 196
Responsibilitv, moral, 183
Restriction of expectation, 65
Ke\, Abel, 2, 5, 9, 14, 46. 69
Ricci, C G . 134, 135
Riddle(s), eternal, 92, insoluble, 93
Riemaiin, G F B , 130, 134, 135, 136
Roman Church, 272, conflict with
topeniie in s)stem, 16, 47, 218, 226,
232, 268, cardinals of, 258
Rougier, L , 48, 49, 202
Russell, Bertrand, 33, 46, 103, 104, 110,
133

Russia, overthrow of Czarist regime, 26,
216 See aho Sonet Union
Ruver, R , 123

Sanity, intellectual, 6
Scale diMSioiis, coincidences of point-
eis and, 107

Scheme, oversmiphfied, 269
Schhclk, Moritz, 26, 38, 48, 83, 105-106,
113, 183, criterion of truth, 28-29,
cognition as establishment of cor-
respondence, 29-30, cooperation w ith
Viennese group, 32-36, “The Turn
in Philosophy,” 41—42, “Space and
Time,” 43, ass.'issinatioii of, 49, vi-
cious philosophi, 49
Scholasticism See School philosophy
School phi’asophy, 8, 78, 94-121, 163,
189, scientific world conception and.

40, tradibons of, 97, new fashionable
form of, 100, truth concept of, 101,
105, logic of, 103-104, time concept
of, 114, conceptions of, 117, disin-
tegration of, 174, 175, 181, social
function, 200

Schioder, 103

Sclirodmger, Edwin, 118, 179, 292, 295,
296

Science(s), absence of boundary points,
111, all-round understanding of, 248,
animistic of Middle Ages, 122, re-
turn to, 194-195, as dynamic living
being, 280, as economical represen-
tation of cxpeiieaccs, 84, as game
with empty sjmbols, 199, bourgeois
conception of, 205, cimpaign against
spirit of, 246, collapse of inneteeiith-
century beliefs, 4, conception of, as
useful technique, 3, crisis of, 215,
critics of, 260, cross connections be-
tween branches of, 273, decadence
of, 125, disontologization, 175, eman-
cipatory lole of, 5, eiolution of, 290,
foundations of, 284, Geiman, 47, 195,
gospel of, 268, heritage of ancient
state of, 238, histoiv of 149, 278,
turning point m, 280, idealistic in-
terpretition of, 195 inherent educa-
tional value, 247, integration of the.
269, 273, 276, intrinsic human values,
261, lacunae for introduction of su-
pcriiatuial factois, 183, limit itions of
sbitcnicnts of, 15, logic of, 220, 23S,
mechanistic failure of, 2-5, M icli’s
debunking of, 18, medieval, oiei-
tlirow of, 223 met iphysieal intei-
pretitioiis of 11, 23, 51, 87, 88, 256
289, 290, org inism of, 62 philosophv
of 45, 50, 220, 253, 273, 277, 27S,
284, cultur il background and, 42, im-
portance of, for political creed, 258,
te idling of, 51, 249-250, 258, train-
ing in, 274, physical 208, public In-
tel est 111 , 262, place of reason in, 289,
position of. 111 cultural life, 256, posi-
tivistic 166, 175, fight against, 195,
piinciples of application of common
sense to, 300, 301, Mach’s and Pom-
car4’s theories, 11-12, pseudo-posi-
tiv ist conception of, 87, pure, 57, 97,

320

index

relabonships with- humambes, 258,
261, 281, 284, philosophy, 4-5, 25,
121, 207, 262, 266, 269, 273, 275,
279, rehgion, 15, 17, 123, 224, 230,
232, 259, return to pre-Galilean, 195,
sociology of, 200, special, binding
materim between, 269, symbobc
structure of, 105, 279, synthesis with
ethics, pohbcs, and rebgion, 271,
teaching of 229, average ihstrucbon,
267, conbibubon of, 278, conven-
tional, 230, courses, 232, gaps m ba-
ditional, 245, 250, 253, improvement
of, 247, pedagogic effort, 217, short-
comings, 231, 249, theorebcal, fun-
damental questions of, 58, badibonal,
84, 88, twentieth-century 25-26, 40,
45, 289, relabsism of, 52, semanbe
significance of, 247, unity of, 35, 36-
33, 79-89, 174, 193, 197, 202, uiii-
\ersal language of, 83, 87, 161, un-
obsersable ilcmtnts in, 39, Victoiian,
184

Science and God (Basink.), 187
Science and llijputhcsis (Poinciie), 53
Science columns, newspaper, 230
Science, Pliilosopli) ind Hcligioii, Con-
feience of, 52

Science student, average, 261
Scientific method, antiscicntific tenden
tits, 2

Scientific piiisuits, cans 1 connection
witli otlier social processes, 200
Scientific world conception, of Vicinii
group, 3S-1S, 68, 92, 94, 108, 112
114

Scienbsin, illusion of, 5
Scientists, educition of future, 258 it-
titude of !e iding 261 contiibution to
political life, 261, nitural, uncLr
domination of philosophy, 266
Self-observation, 166
Semantics, 214, apprnacli, 45 300, m il
adjustment, 241, rules, 244, 246, 291,
analysis, 245, 249, training in, 249
Semites, 148
Sense d ita, 14, 56
Sense perceptions, 68
Senses, evidence of, 145
Sermons, 263
1789, ideas of, 124

Seventeenth century, 290
Shapley, Harlow, 52, 226
Smiphcity, concept of, 176, require-
ments of, 296

Simultaneity, m absolute and relative
sense, 155

Simultaneously, use of, as term, 155
Situabons, complementary, 166, 167
Sixteenth century, 207, 225
Skepbcism, 14, 120, threatemng, 68,
overthrow of enlightenment by, 74-
75

Slogans, debunking empty, 264, gen-
eial, in pohbcs, 266, philosophic, 282
Smuts, General Jan Christiaan, 124
Social phenomena, metaphysical state-
ments as, 34

Social problems, understanding of, 232
Societ}, human, crisis m, 136
Socio ps) chologic approach 250
Sociologists, 253

Sociology, piisitiv istic, eudaemonistic
etliics and, 39, of science, 200, dis-
closes new laws of matter, 202, laws
of, 271, synthesis of physics and, 272
Sommcrfeld, A , 164
Soul, collective, 83, science and the,
125

Soviet Union, 271 establislunent of, 17,
IS, Mich atticked by, 17, 35, 47,
philosoph) of, 35, 47, 88, 125-126,
160, 198-206, 257, anb-Machistic
school, 100, authors quoted, 186,
187-189, 190-192, materialistic lit-
er ihiie, 192

Spice, 112, 26S, measurement of, 19,
22, lour dimeiisiniial, 28, 158, and
mohon, positivistic docbine of, 68,
real, 114, fianie of physical phe-
nomena, 115, 120, Riemanman, 130,
134, 135, 136, form of experience,
180, Euclidein and non-Euchdean,
196, 233, discussions of, 207, empty,
211, absolute, 223, 225, 238, 239,
nature of, 229, 253
“Space and Time” (Schhek), 43
Space-tmie continuum, four-dimen-
sional, 152

Specialisation, cersus ^neral educa-
bon, 261, belief of saenbsts in, ‘273
Speech, material mode of, 162

321

Index

Speeches, on festive occasions, 173
Spencer, Heibert, 212, 214, 257, 302
Spintiuilisni, 81, 124, 126
Spontaneity, of action, 162
Spoon feeding, 281
Stallo, 252, 256
St irs, 225

State of affairs, definition of the, 176
State of a system, 56
Statements, purely logical, 252, intro-
ducing new words, 242, ohserca-
tional, 243, 244, tautological, 243
common-sense, 300
Statistical element, 118
Stohr, Adolf, 58, 71
Straight line, geometiic coiuipt of, 12,
13

Strauss, M , 179

Structural s)stem, 44, in ph\ steal the-
ory, 12-15, in Einstein’s lliioiv, 20
Euclidean and non-EticlidL in 22
Student accrage, of pin sics 203
Studs, E , 62, 65, 66, 6S, 76
Subconscious, 248

Subject, predicate and in school logu
104 obsers mg, 170
Subjectn ism, Mach icci std of, 17
Subject-predicate foim ol judgments
104

Substance, material notion ol, 187
Substantiation, intersubjcilni in imas-
uremeiit, 127, 128
Sun, 226, 227
Sunday sermon, 41

Suptificiality, oierspeciali/atioii and,
259, 273

Supernatural, lacunae in science loi in
troduction of, 183

Svmbols, abstract, 13, in Einstein’s the
oi\, 20, sjstem of, 29-30, 105, 107,
113-114, 120, 243, cognition as sys-
tem ol, 42, experienees and, 106,
118-119, operational meaning of,
248, stiucture of, 278, \alue of, 282,
priiieiples couched in, 283, liave own
hie, 283, choice of, 283
Ssiitaetical differences, between classi-
cal and relativistic mechanics, 155
Syntax, relativistic, formative rules of,
>56, logical^ of Carnap, 162, rules of,
163

Syndiesis, of human knowledge, 271,
of physics and sociology, 272
System, state of a, 56, 120

Tam, llippolyte, 9
Talk, idle philosophic, 264
Tautologies, 110

Teachers, gap in training of, 239-240,
physics, 264

Teaching See Science, teaching of
Technical material stuffing with, 281
Teleological element, in quantum me-
chanics, 128
Television, 262
Tendencies, antiscientific, 2
Teiider-mmded, 218
Tenuis, ordinary rules of, 156
Terminology, question of, 59, Kantian,
180

Terms, vagueness of obsiivalion il, 13
Tencstnal bodies, 221
lest body, 117

‘ Ttstabilitv and Meaiimg” (t 'map),

Textbooks, in Soviet Union, 191, 199,
presentation of Copeinican conflict,
231-232, jahvsics, 234, 235, 264, 278,
non-Euclidean geonietrv, 234, law ol
nieitia, 236, tradition il, 252, cosniol-
og\, 256, di ilcctic d m itciialisin, 272,
current, 280
Theologians, 253
rheology Set Religion
Theories, scientific, metaphysical inter-
prctitions ol, 11, twentieth century,
16, mi t iphv sical, 46 truth of, 107,
matcii ilistic social 136, distiiicUoii
between meclnnstic and matheniati-
crl, 139, distinction between iiitui
tive and abstract, 146, 149, artificial,
153, prescientific, as philosophic
world picture, 160, transition from
mechanisbc to mathematical, 194,
pniduction of, by free imagination,
295

Thing(s), Neurath’s avoidance of word,
35, property of a single, 104, relation
between two, 104, loncept of, 178
Thing m itself, 162
Thing language, 37, 152

322

index

Thinking, progressive, 48, didlccticiil,
203, rational, crisis of, 280
Thomism, 256, 258, 271, 273, 283,
Duhcm’s advocacy of, 16, chief asset
of, 272 See also Neo-Thomism
1 homistie Congress, Rome, 1936, 175
Thomson, J. J , 158, 160, 161
Thought, economy of, 65, agreement
between object and, 98, 102, 105,
disintegration of rational, 121, pure,
umcerse consisting of, 187, dialecti-
cal laws of, as laws for matter, 202,
scientific, rising influence of, 260
Time, 112, 268, measurement of, 19, 22,

114, true, real, 114, framework of,

115, 120, form of experience, 180,
discussions of 207, nature of space
and, 229, absolute, 239, lelatn ity of,
255

Time scale, Einstein, 113
Tolerance, 281
Totalitarian groups, 34
Tough-minded, 218
fiactatus Logtco-Philosophitus (Witt-
genstein), 31-32
Tradition, standard, 271
Tiansformation, logical, 134
Transition from quantity to quality, 202
Trends, American philosophical, 48, re-
ligious, social and political, 248
liiangle, 243, physical, 134, essential
pioperties of, 147

Truth, 295, Schlick’s criteiion of, 28-29,
Hcichcnbach’s ciiterion of, 31, philo-
sophical 91, piactic.d and theoretical
conceptions of, 102, an invention,
102, criteria of, 102, 108, 219, 222,
223, 251, absurdity of pragmatic con-
cept of, 104, eternal, 114, 115, con-
cictc, 200, 203, scientific and philo-
sophic, 209, 211, 220, mathematical,
211, two conceptions of, 219, dis-
crepancy between mathematical and
philosopinc, 222, relativity of, 230,
scientific and philosophic, 251
“Turn in Philosophy, The” (Schlick),
41

Twelfth century, 221
Twentieth century, 224-227, 256, 261,
286, physical theoiies of, 123-137,
physictd research, 149, antiscientific

ideology, 230, obscure domain of tlie-
oiics, 241

Uncutainty, piinciple of, 168, 240, 275
Unconscious, unfulfilled longmg m, 159
Under the Banner of Marxism, 191
Understandmg, conception of, 32, em-
pithic, 197, casual, 213
Undeistandmg Science (Conant), 50
Unified field theories, 295
Unified scheme, 301
United States, 33, 44, 48, 50
Unity, lost, of nature, 159
Unity of science, 35, 36-38, 79-89, 174,
193, 197, 202

Unity of Scieiiie, Congress fin the, 49
Universe, “truth” about, 4, mathema-
tician’s conception of, 124, spiiitual-
istic conception of, 160, consisting of
pure tlioiight, 187, true picture of,
222, central stage of, 227, master of,
227, democratic order of, 227, intel-
ligible by analogy, 298
Universities, German, 34
Utopianism, 65

Vagueness, 243
Vaminger, H , 43-44
Valentinov , N , 190
Validity, eternal, 215, 280
Value(s), emotional, 59, judgments of,
77, observed and calculated, 107,
exact, 115, 116, educational, 284
Value of Science, The (Pomcare), 53
Variables, fictitious state, 60
Velocity, initial position and, of elec-
tron, 118, with respect to the ether,
154, 155, new syntax for, 179
Venfication, operabonal, 43, direct ex-
perimental, 140
Vibrations, of a medium, 120
Vienna, City of, 31, 48
Vienna, University of, 1, 2, 32, 47, 49
Vienna Circle, 1-2, 31, 33, 34, 49, 79,
85, 86, 133, 160, 172, 203, coopera-
tion of Schlick and Carnap, 32-36,
elimination of metaphysics, 34-35,
unification of science, 36-38, at-
tacked as anbphilosophic, 175 See
also Scientific world ooncepbon ,
Viennese waltz, 38

323

Index

Viewpoint, prcpositivistic and prescien-
tific, 42

Visualizable theory, 146

Vitalism, question oi mechanism or, 60;

spiritualistic, 168
Voltaire, Frangois Arouet, 72, 75
Vouillcmin, General C. E., 49

War, causes of, 260
Wave functions, 118, 202
Wave mechanics, 118, 131
Weimar Republic, 26
Wells, H. G., 228-229, 232, 341
Weltanschauung, 38
Wcltauffassung, 38
Wenzl, Aloys, 189
Wliilchcad, A. N., 265, 266, 300
Wine, new, into old bottles, 25, 40
WittRcnstein, L., 26, 31-32, 48, 103.
112, 133, 256

Words, Neurath’s index of prohibited,
35; of everyday life, 244
tVorfd, mechanistic and organismic con-
ceptions of, 3, 4; scientific and mech-
anistic viorvs of, 6-7, 58; structure of.

in Einstein’s theory, 20; Gentral Eu-
ropean movement toward scientific
conception of, 26; apparent and real,
39, 77. 80. 81, 134, 160, 163, 181,
103; transcendental, 104; logical
structure of. 111; outer, 112; mathe-
matical, 123; organismic conception
of, 126; built according to pure math-
ematics, 132-134; mystical concep-
tions of, 133; idealistic picture of,
136; of atomic physics, 157; real
metaphysical, 161; material, neglect
of, 161; pin'sical, 243
World architect, 133
World creator, l33, 136
World conception, in ctliical-rcligious
sense, 60. Sec also Scientific world
conception

World pictnie, iSi); of priniitirc man,
SO; pu'seientific ihcoiies as philo-
sophic, 160

World system. See Copernican system,
Ptolemaic system

World view, idealistic, 158, 186; de-
cline of rational, 287
World War 1, 18

324

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